4. (40 pts) Using the accompanying figure answer the following questions showing

Question

4. (40 pts) Using the accompanying figure answer the following questions showing how you arrived at every single answer. I. The consumer is optimizing at point A in the accompanying figure. The price of good X is $5. a. (5 pts) What is the consumer's income? b. (5 pts) What is the price of good Y? c. (5 pts) What is the Market Rate of Substitution between X and Y? d. (5 pts) At point A, how many units of X does the consumer purchase? e. (5 pts)At point A, what is the Marginal Rate of Substitution between X and Y? II. Suppose the budget line changes so that the consumer equilibrium moves from point A to point B. f. (5 pts) What change in the environment led to this new equilibrium? (give specific numbers) g. (5 pts) Is the consumer better off or worse off as a result of this change? why? h. (5 pts) Are X and Y substitutes or complements? Why?

Explanation / Answer

            a) At point A, consumer’s Income is the budget constraint which is given as

M = X*Px + Y*Py

At point on the Budget Line, where Y = 0, the consumer consumes all of X

Thus, according to the Budget Line shown, M = 30*5 = 150.

b) Now we know M = 150, At point on the Budget Line,where a person consumes all of Y, and no X, then we have

150 = 20*Py

Thus, Py = 7.5.

c) Marginal Rate of Substitution can be given as,

MRS = - Px/Py

Thus, MRS = - 5/7.5

                  = 0.6667

d) At point A, consumption of Y= 10 units

Thus using M = X*Px + Y*Py

We have, 150 = X*5 + 10*7.5

X = 15

e) The MRS will be the same as calculated in (c) MRS = - Px/Py

Thus, MRS = - 5/7.5

                  = 0.6667

f) A reduction in price of good Y has led to an outward shift in the Budget Line.

Now we know M = 150, At point on the Budget Line,where a person consumes all of Y, and no X, then we have

150 = 30*Py

Thus, Py = 5.

Thus, price good Y has reduced by $2.5 to $5.

g) The consumer is better-off as the consumer moves to a higher Indifference Curve, i.e. from I to II, thus raising the utility.

h) Goods X and Y are substitutes, as with a reduction in price of Y, the consumer reduces the consumption of good X and substitute it by raising the consumption of good Y in moving from point A to B.

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