Question 1

In an exchange economy A's utility is given by U_A = x + y and B's by U_B = min[x,2y].The initial endowment for A is x = 10,y = 8 and for B,x = 8,y = 4.To reach the contact curve,these individuals must:

Accepted Answer

To determine if they are on the contract curve, we need to check if the marginal rates of substitution (MRS) are equal. A's MRS is the ratio of the marginal utilities of x and y, which is 1 since A's utility function is additive and symmetric in x and y. B's MRS is the ratio of the marginal utilities of x and y, but given B's utility function is min[x,2y], B's MRS will depend on the specific allocation of goods. Initially, B's utility is determined by x (since x < 2y), making B's MRS effectively 1 (the ratio of the marginal utility of x to y, both of which contribute equally to utility in this region). Since both A and B have an MRS of 1 with their initial endowments, they are already at a point where their MRSs are equal, indicating they are on the contract curve. No trade is necessary to reach an efficient allocation.

Question 2

Suppose two individuals in an exchange economy have identical utility functions given by Person A has an endowment of x = 9 y = 8,person B has one of x = 16 y = 2.The price ratio that will prevail in equilibrium is:

Accepted Answer

In equilibrium, individuals will equate their marginal rate of substitution to the price ratio. The marginal rate of substitution for both individuals is given by MRS = -2x/y. Therefore, for person A, MRS = -2(9)/8 = -2.25 and for person B, MRS = -2(16)/2 = -16. They will trade until the price ratio is equal to the ratio of their marginal rates of substitution. Thus, (p_x / p_y) = 2.25/16 = 0.14. Therefore, the closest answer choice is C with p_x / p_y = 0.4.

Question 3

Suppose that the two persons in an exchange economy (A and B)have utility functions given by Along the contract curve,B's ratio of Y to X will be:

Accepted Answer

The contract curve represents the set of points where both individuals have equal marginal rates of substitution (MRS). At any point on the contract curve, the slope of the indifference curve for A must equal the slope of the indifference curve for B.

Taking the partial derivative of the utility function for A with respect to Y/X, we get:

dU/d(Y/X) = 11(Y/X)^2

Similarly, taking the partial derivative of the utility function for B with respect to Y/X, we get:

dU/d(Y/X) = 22(X/Y)

Setting these two expressions equal to each other (since they represent the MRS for A and B, respectively), we get:

11(Y/X)^2 = 22(X/Y)

Simplifying this equation, we get:

(Y/X)^3 = 2

Taking the cube root of both sides, we get:

Y/X = (2)^(1/3)

So B's ratio of Y to X on the contract curve will be approximately 1:2. Hence, the answer is C) 1:2.

Question 4

In a two-good exchange economy,A's utility is given by  And B's utility by  Along the contract curve,x/y for B will be times x/y for A.

Accepted Answer

The answer of In a two-good exchange economy,A's utility is...

Quiz 11: General Equilibrium and Welfare

In an exchange economy A's utility is given by U_A = x + y and B's by U_B = min[x,2y].The initial endowment for A is x = 10,y = 8 and for B,x = 8,y = 4.To reach the contact curve,these individuals must:

Suppose two individuals in an exchange economy have identical utility functions given by Person A has an endowment of x = 9 y = 8,person B has one of x = 16 y = 2.The price ratio that will prevail in equilibrium is:

Suppose that the two persons in an exchange economy (A and B) have utility functions given by Along the contract curve,B's ratio of Y to X will be:

In a two-good exchange economy,A's utility is given by And B's utility by Along the contract curve,x/y for B will be times x/y for A.

Quiz 11: General Equilibrium and Welfare

In an exchange economy A's utility is given by UA = x + y and B's by UB = min[x,2y].The initial endowment for A is x = 10,y = 8 and for B,x = 8,y = 4.To reach the contact curve,these individuals must:

Suppose two individuals in an exchange economy have identical utility functions given by Person A has an endowment of x = 9 y = 8,person B has one of x = 16 y = 2.The price ratio that will prevail in equilibrium is:

Suppose that the two persons in an exchange economy (A and B) have utility functions given by Along the contract curve,B's ratio of Y to X will be:

In a two-good exchange economy,A's utility is given by And B's utility by Along the contract curve,x/y for B will be times x/y for A.

In an exchange economy A's utility is given by U_A = x + y and B's by U_B = min[x,2y].The initial endowment for A is x = 10,y = 8 and for B,x = 8,y = 4.To reach the contact curve,these individuals must: