Question

Suppose that the utility you receive from buying vegetables (V) and medicine (M) are given by: ???????(?, ?) = 4? ^0.8?^0.2)

a) What is your marginal utility of vegetables and medicine?

b) What is your marginal rate of substitution (vegetables as x good and medicine as y good) between the two?

c) If the price of vegetables is $20, the price of medicine is $15, and income is $120, what is your optimal consumption of V and M? Graphically show your answer.

d) If we start to tax medicine, increasing the price to $20, solve for your new optimal consumption of V and M . Given this utility function, how is your answer “predictable” based on your answer to c?

e) How much utility to you generate from the optimal bundles found in parts (c) and (d)?

Answer 1

THE STEP BY STEP WORKING IS AS FOLLOWS-

FIRST WE SOLVED FOR MU BY DIFFERENTIATING THE UTILITY THEN USING IT WE DERIVED MRS AND A RELATION BETWEEN M AND V

AFTER THAT WE DERIVED THE OPTIMAL BUNDLES AS MARKED IN BOXES THEN WE FOUND THE VALUES OF IT AND GRAPHED IT

AFTER THAT WITH NEW PRICE OF M WE FOUND THE NEW BUNDLE

IT WAS PREDICTABLE FROM C AS WE CAN SEE THAT THE OPTIMAL BUNDLE OF V REMAINS SAME AND ONLY M IS CHANGING. ALSO THE RELATION BETWEEN M AND PRICE OF M IS INVERSELY PROPOTIONAL SO AS PRICE INCREASES M FALLS.

AT THE END WE FOUND THE UTILITIES FROM BOTH THE BUNDLES AS SHOWN ABOVE.

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