Question 1

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the average variable cost is

Accepted Answer

The average variable cost (AVC) is found by dividing the variable costs by the quantity (q). In the given cost function TC = Aq³ + bq² + cq +d, the variable costs are all terms that include q (the first three terms), and the fixed cost is d. When calculating AVC, we exclude fixed costs (d) and divide each variable term by q, resulting in Aq² + bq + c.

Question 2

Suppose that a lawn mowing services production function for lawns mowed in a week is M = (LK)1/2,where L is labor hours and K is the amount of capital (mowers and trimmers).The expansion path depends on

Accepted Answer

The expansion path shows the combinations of labor and capital that result in the same level of output. The shape of the expansion path depends on both the wage rate, which affects the cost of labor, and the rental rate, which affects the cost of capital. Therefore, the answer is C.

Question 3

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K)is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the fixed cost is

Accepted Answer

Fixed costs are costs that do not change with the level of output. Since capital (K) is fixed at 100 and the rental rate on capital is $20, the fixed cost is 100 * $20 = $2,000.

Question 4

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the total fixed cost is

Accepted Answer

Total fixed costs are those costs that do not vary with the level of output. In the given cost function TC = Aq³ + bq² + cq +d, the term "d" does not depend on the quantity (q) and thus represents the total fixed cost.

Question 5

Suppose pigs (P)can be fed corn-based feed (C)or soybean-based feed (S)such that the production function is P = 2C + 5S.If the price of corn feed is $4 and corn feed is on the horizontal axis,and the price of soybean feed is $5 and soybean feed lies on the vertical axis,what is expansion path?

Accepted Answer

The answer of Suppose pigs (P)can be fed corn-based feed...

Question 6

Suppose MPL = 40 and MPK = 20 and the rental rate on capital is $10. If the level of production is currently efficient,the wage rate must be

Accepted Answer

In an efficient level of production, the ratio of the marginal product of labor (MPL) to the wage rate (W) should equal the ratio of the marginal product of capital (MPK) to the rental rate of capital (R). Given MPL = 40, MPK = 20, and R = $10, we can set up the equation 40/W = 20/10. Solving for W gives us W = $20.

Question 7

Suppose the production function for coffee (C)is C = min(B,W),where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The cost minimizing combination of beans and water for C = 200 is

Accepted Answer

To minimize costs, we need to choose the input that is cheaper per unit. 
- Cost of beans = $10 per pound 
- Cost of water = $0.10 per gallon

For C = 200, we want to produce exactly 200 units of coffee. Using the production function, we can write: 
C = min(B,W) 
200 = min(B, W)

Since we want to minimize costs, we need to choose the input that is cheaper per unit. In this case, water is cheaper per unit, so we should choose W to be as small as possible.

To produce 200 units of coffee, we need to use at least 200 gallons of water. If we use any less, we won't be able to produce 200 units of coffee.

So the cost-minimizing combination is: 
C = 200 
B = min(B,W) = min(200, W) 
W = 200 gallons (the minimum amount needed to produce 200 units of coffee)

We can check that this combination satisfies the production function: 
C = min(B,W) = min(200,200) = 200

The cost of this combination is: 
Cost = Cost of beans + Cost of water 
Cost = $10 per pound x B + $0.10 per gallon x W 
Cost = $10 per pound x min(200, W) + $0.10 per gallon x 200 
Cost = $10 per pound x 200 + $0.10 per gallon x 200 
Cost = $2000 + $20 
Cost = $2020

Therefore, the best choice is D, with B = 200 pounds and W = 200 gallons.

Question 8

Suppose pigs (P)can be fed corn-based feed (C)or soybean-based feed (S)such that the production function is P = 2C + 5S.The expansion path depends

Accepted Answer

The expansion path depends on the relative prices of corn-based and soybean-based feed. If the price of corn-based feed is less than 2/5 the price of soybean-based feed, then it will be more efficient to use corn-based feed. If the price of corn-based feed is greater than 2/5 the price of soybean-based feed, then it will be more efficient to use soybean-based feed. Therefore, the best choice depends on the prices of the two feeds.

Question 9

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K)is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run marginal cost is

Accepted Answer

The short run marginal cost (MC) is derived from the total cost (TC) function, which in turn is based on the production function. In the short run, with capital fixed, the only variable input is labor. The cost of labor is the wage rate times the amount of labor used. The MC is the derivative of the TC with respect to quantity produced (q). Given the production function and the fixed capital, the correct formula for MC, without knowing the specific form of the production function, involves the relationship between q and the inputs. The choice $\frac { 3 q ^ { 2 } } { 100 }$ suggests a specific relationship between output and input costs that could be derived from a given production function, assuming labor is the variable input and its cost is incorporated. This choice implies a quadratic relationship between output and costs, which is plausible given the information provided.

Question 10

Suppose pigs (P)can be fed corn-based feed (C)or soybean-based feed (S)such that the production function is P = 2C + 5S.If the price of corn feed is $2 and the price of soybean feed is $6,what is the cost-minimizing fee combination producing P = 200?

Accepted Answer

The answer of Suppose pigs (P)can be fed corn-based feed...

Question 11

Suppose the production function for coffee (C)is C = min(B,W),where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The expansion path

Accepted Answer

The production function C = min(B,W) indicates a fixed-proportion production process, meaning the expansion path is determined by the ratio of inputs, not their prices.

Question 12

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the average total cost is

Accepted Answer

The formula for average total cost is Total Cost (TC) divided by the quantity produced (q). Therefore, we can simplify the given cost function by dividing it by q: TC/q = Aq² + bq¹ + cq/q + d/q The last term, d/q, can be written as a constant cost per unit. Therefore, the average total cost is: ATC = Aq² + bq¹/q + cq/q + d/q Simplifying the second term further, we get: ATC = Aq² + bq² + cq/q + d/q Combining the constant terms, we finally get: ATC = Aq² + bq + cq/q + d/q Therefore, the correct answer is (A).

Question 13

Suppose the production function for coffee (C)is C = min(B,W),where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The expansion path is

Accepted Answer

The production function for coffee is C = min(B,W), which means that the amount of coffee produced depends on the minimum of the amount of beans and water used in the production process.

Since the price of water is $.10 per gallon and the price of beans is $10 per pound, the cost of producing coffee can be expressed as:

Cost = 10B + 0.1W

To find the optimal combination of beans and water, we need to minimize the cost of production subject to the production function C = min(B,W).

If we assume that the price of water is fixed, then the optimal choice of B and W can be found by simply setting the partial derivative of the cost function with respect to B equal to zero, which gives:

10 = λ    (where λ is the Lagrange multiplier)

Similarly, setting the partial derivative of the cost function with respect to W equal to zero gives:

0.1 = λ

Substituting λ = 10 into the production function C = min(B,W) gives us:

C = min(B,W) = min(B, 10)

Therefore, the optimal choice is to use as many beans as possible, subject to the constraint that we must use 10 times more water.

This gives us the following expansion path:

B = 10W

Question 14

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K)is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run average cost is

Accepted Answer

The short-run average cost (SAC) in production economics includes both fixed costs and variable costs. Fixed costs are those that do not change with the level of output, such as the rental rate on capital when the capital is fixed. Variable costs change with the level of output, such as costs associated with labor if labor is the variable input. The SAC can be represented as the sum of average fixed costs (AFC) and average variable costs (AVC). Given that capital (K) is fixed at 100 and the rental rate on capital is $20, the total fixed cost (TFC) is 100 * $20 = $2,000. The AFC is TFC divided by quantity (q), which is $2,000 / q. Without specific information on the variable costs or the functional form relating output to labor input, we cannot directly calculate the AVC or the part of the SAC that varies with q. However, the given option A, $\frac { 2,000 } { q } + \frac { q ^ { 2 } } { 100 }$, correctly represents a structure where there's a component that decreases with increasing q (representing the spreading out of fixed costs over more units) and a component that increases with q, possibly representing increasing variable costs with output. This structure is consistent with typical short-run average cost curves in economics.

Question 15

Suppose MPL = 20 and MPK = 40 and the rental rate on capital is $10. If the level of production is currently efficient,the wage rate must be

Accepted Answer

To determine if the current level of production is efficient, we can use the formula MPL/PL = MPK/PK, where PL is the wage rate and PK is the rental rate on capital.

Substituting the given values, we get:

20/PL = 40/10
20/PL = 4
PL = 5

Therefore, the wage rate must be $5 for the current level of production to be efficient. Answer choice B is the correct choice.

Question 16

The opportunity cost of producing a bicycle refers to

Accepted Answer

The opportunity cost of producing a bicycle refers to the value of the goods that were given up to produce the bicycle. This includes the cost of the resources that could have been employed in producing an alternative product. Option A is incorrect because it only refers to the out-of-pocket payments made in the production process. Option C is incorrect because the bicycle's retail price is determined by various other factors such as demand, supply, and marketing. Option D is incorrect because the marginal cost only considers the additional cost of producing one more bicycle, whereas opportunity cost considers the value of the forgone alternative.

Question 17

Suppose pigs (P)can be fed corn-based feed (C)or soybean-based feed (S)such that the production function is P = 2C + 5S.If the price of corn feed is $4 and the price of soybean feed is $5,what is the cost-minimizing feed combination producing P = 200?

Accepted Answer

The answer of Suppose pigs (P)can be fed corn-based feed...

Question 18

Suppose pigs (P)can be fed corn-based feed (C)or soybean-based feed (S)such that the production function is P = 2C + 5S.If the price of corn feed is $2 and the price of soybean feed is $5,what is the cost-minimizing feed combination producing P = 100?

Accepted Answer

Given the production function P = 2C + 5S and the goal to produce P = 100, the cost-minimization problem involves finding the combination of C and S that minimizes cost while producing the required amount of output. The cost of using corn-based feed (C) is $2 per unit, and the cost of using soybean-based feed (S) is $5 per unit. The statement that all points on the P = 100 isoquant, including those listed in options A, B, and C, would cost the same, implies that any combination of C and S that satisfies the production function P = 100 will have the same total cost. This is because the production function and the prices of inputs are linear, leading to a situation where the isoquant for P = 100 is a straight line, and the isocost lines are also straight and parallel to the isoquant, indicating that multiple combinations of C and S can produce 100 units of P at the same total cost.

Question 19

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K)is fixed at 100.If the wage is $10 and the rental rate on capital is $20,the short run production function is

Accepted Answer

In the short run, capital (K) is fixed at 100. Substituting K = 100 into the production function q = K^1/2 * L^1/3 gives q = (100)^1/2 * L^1/3 = 10L^1/3.

Question 20

The accountant's cost of producing a bicycle refers to

Accepted Answer

The accountant's cost of producing a bicycle refers to the out-of-pocket payments made to produce the bicycle, such as the cost of materials, labor, and other direct expenses. It does not include the value of goods that were given up or opportunity costs, which are considered in economic costs. The retail price of the bicycle is determined by various factors such as demand, supply, competition, and profit margin, and is not the same as the accountant's cost. The marginal cost of the last bicycle produced refers to the additional cost incurred in producing one more unit, which is not the same as the total cost or accountant's cost of production.

Quiz 7: Costs

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the average variable cost is

Suppose that a lawn mowing services production function for lawns mowed in a week is M = (LK) 1/2,where L is labor hours and K is the amount of capital (mowers and trimmers) .The expansion path depends on

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the fixed cost is

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the total fixed cost is

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $4 and corn feed is on the horizontal axis,and the price of soybean feed is $5 and soybean feed lies on the vertical axis,what is expansion path?

Suppose MPL = 40 and MPK = 20 and the rental rate on capital is $10. If the level of production is currently efficient,the wage rate must be

Suppose the production function for coffee (C) is C = min(B,W) ,where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The cost minimizing combination of beans and water for C = 200 is

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.The expansion path depends

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run marginal cost is

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $2 and the price of soybean feed is $6,what is the cost-minimizing fee combination producing P = 200?

Suppose the production function for coffee (C) is C = min(B,W) ,where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The expansion path

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the average total cost is

Suppose the production function for coffee (C) is C = min(B,W) ,where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The expansion path is

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run average cost is

Suppose MPL = 20 and MPK = 40 and the rental rate on capital is $10. If the level of production is currently efficient,the wage rate must be

The opportunity cost of producing a bicycle refers to

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $4 and the price of soybean feed is $5,what is the cost-minimizing feed combination producing P = 200?

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $2 and the price of soybean feed is $5,what is the cost-minimizing feed combination producing P = 100?

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100.If the wage is $10 and the rental rate on capital is $20,the short run production function is

The accountant's cost of producing a bicycle refers to

Quiz 7: Costs

Suppose a cost function is TC = Aq3 + bq2 + cq +d. Then the average variable cost is

Suppose that a lawn mowing services production function for lawns mowed in a week is M = (LK) 1/2,where L is labor hours and K is the amount of capital (mowers and trimmers) .The expansion path depends on

Suppose a production function is q = K1/2L1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the fixed cost is

Suppose a cost function is TC = Aq3 + bq2 + cq +d. Then the total fixed cost is

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $4 and corn feed is on the horizontal axis,and the price of soybean feed is $5 and soybean feed lies on the vertical axis,what is expansion path?

Suppose MPL = 40 and MPK = 20 and the rental rate on capital is $10. If the level of production is currently efficient,the wage rate must be

Suppose the production function for coffee (C) is C = min(B,W) ,where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The cost minimizing combination of beans and water for C = 200 is

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.The expansion path depends

Suppose a production function is q = K1/2L1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run marginal cost is

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $2 and the price of soybean feed is $6,what is the cost-minimizing fee combination producing P = 200?

Suppose the production function for coffee (C) is C = min(B,W) ,where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The expansion path

Suppose a cost function is TC = Aq3 + bq2 + cq +d. Then the average total cost is

Suppose the production function for coffee (C) is C = min(B,W) ,where B = beans in pounds and W = water in gallons. Suppose the price of water is $.10 per gallon and the price of beans is $10 per pound.The expansion path is

Suppose a production function is q = K1/2L1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run average cost is

Suppose MPL = 20 and MPK = 40 and the rental rate on capital is $10. If the level of production is currently efficient,the wage rate must be

The opportunity cost of producing a bicycle refers to

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $4 and the price of soybean feed is $5,what is the cost-minimizing feed combination producing P = 200?

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S.If the price of corn feed is $2 and the price of soybean feed is $5,what is the cost-minimizing feed combination producing P = 100?

Suppose a production function is q = K1/2L1/3 and in the short run capital (K) is fixed at 100.If the wage is $10 and the rental rate on capital is $20,the short run production function is

The accountant's cost of producing a bicycle refers to

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the average variable cost is

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the fixed cost is

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the total fixed cost is

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run marginal cost is

Suppose a cost function is TC = Aq³ + bq² + cq +d. Then the average total cost is

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run average cost is

Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K) is fixed at 100.If the wage is $10 and the rental rate on capital is $20,the short run production function is