Question

After a hard day of classes, Joe frequently enjoys going out to dinner at the Slick Pig or bowling at Strike and Spare. Both activities cost $5. Assume he has $50 per month entertainment budget. Find Joe's optimal consumption bundle of barbecue and bowling and GRAPHICALLY show this optimum on a diagram that shows (and labels) the indifference curves and budget constraint. In the utility functions, S indicates trips to the Slick Pig and B indicates trips to Strike and Spare bowling.

a. U = 2S+B

b. U= min{S,B}

Answer 1

P_S= $5

P_B = $5

Income , I = $50.

(a) U= 2S + B

MRS = MU_S/ MU_B

MU_S = 2

MU_B =1

MRS = 2/1 = 2.

It implies that the slope of the indifference curve is constant = 2.

And budget equation is P_S S + P_B B = I

5 S + 5 B = 50

When S= 0, B =10

When B=0 , S=10

Optimal bundle is where budget line is tangent to the indifference curve , here the indifference curve slope is constant. It implies that there would be corner solution.Optimal bundle is when Joe consumes 10 units of B i.e 10 trips to strike and spare and consumes no S i.e no trips to the slick pig . This is shown in the figure below:

(b) U = min(S,B)

At optimal S=B

Now, by putting this into budget equation , we get:

5 S + 5 S = 50

10 S = 50

S= 5 . And hence, B=5 .

Hence, optimal bundle is when Joe consumes 5 units of S i.e 5 trips to slick pig and 5 units B i.e 5 trips to strike and spare. This is shown in the figure below: