Our old friend, Edmund Stench, of Chapter 2 loves punk rock video tapes.He has no income and therefore has to accept garbage in his backyard in return for money.Each video tape cost $2 and each sack of garbage that he accepts brings him $1.His utility function is given by U(c, g)= min{2c, 20 - g}, where c is the number of video tapes and g is the number of sacks of garbage that he gets per month.Each month he will choose to accept

Question

Quizplus · Accepted Answer

In order to determine the best choice for Edmund, we need to find the combination of c (number of video tapes) and g (number of sacks of garbage) that maximize his utility function, given his constraints (no income and a limited number of sacks of garbage he can accept each month).

First, let's look at the utility function itself. The function is a Cobb-Douglas function, which means that the marginal utility of each input (c and g) is decreasing as the quantity of that input increases. This reflects the law of diminishing marginal utility in economics.

The function has a minimum function, which means that we need to find the minimum value of the function in order to maximize Edmund's utility. We can simplify the function by taking its natural logarithm:

ln(U) = ln(c) + 0.5 ln(g) - 10 ln(20 - g)

We can then take the partial derivatives of ln(U) with respect to c and g:

∂ ln(U)/∂c = 1/c
∂ ln(U)/∂g = 0.5g/(20 - g)

Setting these equal to zero and solving for c and g, we get:

c = 1
g = 10

However, we need to check whether these values satisfy Edmund's constraints. The cost of one video tape is $2, so he needs to collect at least $2 to be able to buy one tape. The revenue from accepting 10 sacks of garbage is $10. Therefore, he can buy at most 5 video tapes per month. Since c = 1 is less than 5, it satisfies the constraint.

Therefore, the best choice for Edmund is to accept 10 sacks of garbage per month and use the $10 revenue to buy one video tape.

Our Old Friend, Edmund Stench, of Chapter 2 Loves Punk