Question

Linda loves buying shoes and going out to dance. Her utility function for pairs of​ shoes, S, and the number of times she goes dancing per​ month, T,​ is: ​U(S, T)​ = 2ST with marginal​ utilities: MUS​ = 2T and MUT​ = 2S. It costs Linda ​$ to buy a new pair of shoes or to spend an evening out dancing. Assume that she has ​$ to spend on shoes and dancing. ​
1.) Use the line drawing tool to draw​ Linda's budget line. Label this line​ 'Budget'. ​
2.) Use the point drawing tool to locate​ Linda's optimal consumption bundle. Label this point​ 'R'. Carefully follow the instructions​ above, and only draw the required objects.

Answer 1

Answer:

See Explanation

Explanation:

Given

$U(S,T) = 2ST$

$M_U_S =2T$

$M_U_T=2S$

The following details are omitted from the question

$P_S= \ 50$ --- Price of the Shoes

$P_T = \ 50$ --- Spent on dancing

$B = \ 500$ --- Budget on shoe and dancing

Solving (a): Her budget line

First, we determine her budget equation (B).

This is calculated by:

$B = P_S * S + P_T *T$

This gives:

$500 = 50 * S + 50 * T$

$500 = 50 S + 50 T$

Divide through by 50

$10 =S + T$

$S + T = 10$ --- The budget equation

See attachment for the budget line equation

Solving (a): Optimal Consumption Bundle Point

First, we determine the marginal rate of substitution (MRS) using:

$MRS = \frac{MU_s}{MU_t} = 1$

$MRS = \frac{2S}{2T} =1$

This implies that:

$\frac{2S}{2T} = 1$

Cross Multiply

$2S = 2T * 1$

$2S = 2T$

Divide by 2

$S = T$

Substitute T for S in the budget equation

$T + T= 10$

$2T = 10$

$T=5$

Recall that:

$S = T$

$S = 5$

So, the point if optimal consumption bundle is (5,5)

See attachment for point R