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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.

Respuesta :

MrRoyal

Answer:

See Explanation

Explanation:

Given

[tex]U(S,T) = 2ST[/tex]

[tex]M_U_S =2T[/tex]

[tex]M_U_T=2S[/tex]

The following details are omitted from the question

[tex]P_S= \$50[/tex] --- Price of the Shoes

[tex]P_T = \$50[/tex] --- Spent on dancing

[tex]B = \$500[/tex] --- Budget on shoe and dancing

Solving (a): Her budget line

First, we determine her budget equation (B).

This is calculated by:

[tex]B = P_S * S + P_T *T[/tex]

This gives:

[tex]500 = 50 * S + 50 * T[/tex]

[tex]500 = 50 S + 50 T[/tex]

Divide through by 50

[tex]10 =S + T[/tex]

[tex]S + T = 10[/tex] --- 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:

[tex]MRS = \frac{MU_s}{MU_t} = 1[/tex]

[tex]MRS = \frac{2S}{2T} =1[/tex]

This implies that:

[tex]\frac{2S}{2T} = 1[/tex]

Cross Multiply

[tex]2S = 2T * 1[/tex]

[tex]2S = 2T[/tex]

Divide by 2

[tex]S = T[/tex]

Substitute T for S in the budget equation

[tex]T + T= 10[/tex]

[tex]2T = 10[/tex]

[tex]T=5[/tex]

Recall that:

[tex]S = T[/tex]

[tex]S = 5[/tex]

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

See attachment for point R

Ver imagen MrRoyal

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