Question

A consumer has an income of $3,000. Wine costs $3 per glass, and cheese costs

    $6 per pound.

               

     a. (0.5 pt) Draw the consumer’s budget constraint with wine on the vertical axis.

                        (Make sure to label the axes.)

    

     b. (0.1 pt) What is the slope of the budget constraint?

    c. (0.1 pt) On the graph for part a, draw an indifference curve illustrating an optimum

                        bundle (point K).

     d. (0.4 pt) The consumer now gets a raise. So, her income increases from $3,000 to

                        $4,000.

                        → Show what happens if both wine and cheese are normal goods with

                               a new optimum bundle (point Q). What happens to the consumption of

                             wine and cheese?

                        → Then, show what happens if cheese is an inferior good with a new

                             optimum bundle (point R). What would happen to the consumption of wine

                             and cheese in this case?

        

     e. (0.3 pt) The consumer’s income is $3,000 again. However, the price of cheese has

                        risen from $6 to $10 per pound, while the price of wine remains $3 per

                        glass. Show what happens to the consumption of wine and cheese with a

                        new optimum bundle (point T).

Answer 1

(a) Budget constraint: 3,000 = 3W + 6C, or 1,000 = W + 2C, where W, C: Quantity of wine and cheese respectively

When C = 0, W = 1,000 (Vertical intercept) & when W = 0, C = 1,000/2 = 500 (Horizontal intercept).

In following graph, AB is the budget line.

(b) Slope of budget line = -Pc/Pw = -6/3 = -2

(c) Optimal bundle K is the point where indifference curve IC1 is tangent to AB with optimal bundle being W1 & C1.

(d) New budget line: 4,000 = 3W + 6C

When C = 0, W = 4,000/3 = 1,333.33 (Vertical intercept) & when W = 0, C = 4,000/6 = 666.67 (Horizontal intercept).

In above graph, EF is the new budget line.

When both are normal goods, quantity of both will increase to (W2, C2) as shown by point Q where new indifference curve IC2 is tangent to EF.

When cheese is inferior good, quantity of wine will increase but quantity of cheese will decrease as shown by point R with new bundle being (W3, C3) where new indifference curve IC3 is tangent to EF.

NOTE: As per Answering Policy, 1st 4 parts are answered.