1. In all these problems, the consumer is choosing to spend all his income on either pizza or Dr. Pepper. In all graphs, put Dr. Pepper on the vertical axis.

a) Draw the budget of a person who has $150 and Dr. Pepper costs $2 per unit and pizza costs $15 per unit specifically labeling the intercepts. Explain whether or not it is possible for the consumer’s utility maximizing bundle to be 7 pizzas and 30 Dr. Peppers

b) There is a demand curve of pizza for this individual contains the following 2 points:
P Q
$10 6
$5 12

This person has $150 in income and chooses to buy 30 Dr. Peppers when the price of pizza is $10 and when the price of pizza is $5. Draw the budget constraint when the price of pizza P = $5 and when the price of pizza P = $10. Draw both of these budget constraints together on a new graph, but not the same graph as in (a). Specifically label the intercepts of each constraint. Find the coordinates of the utility maximizing point on each budget and draw the indifference curve through the point. Finally, find the MRS at each of the optimal points.

c) If we knew that, for the budget in (a) the utility maximizing bundle contained 4 pizzas, would this information tell us a 3rd point on the demand curve in (b)? Why or why not.

2. Consider a consumer with $10 to spend on these two goods where the price of apples is always $2 each.

Apples Oranges
Q    U Q    U
1    50 1    30
2    75 2    56
3    85 3    78
4    90 4    96
5    92 5    108
6    93 6    116

a) Find the utility maximizing combination of apples and oranges if oranges cost $4 each. Explain why the consumer didn’t choose the bundle of 3 apples and 4 oranges.

b) Repeat all of part (a) if oranges cost $1 each.

3. Let’s explore the business of Farmer Ted. The farmer has two fixed inputs that he owns: A tractor, which Ted can rent out for $24000 per year if he doesn’t use it on his farm at all in the year, and land which is currently valued at 1 million dollars. The only variable input is labor. The output of the farm per year depends on the quantity of labor hired per year in the following way:
L Q L Q
1 10,000 6 90,000
2 25,000 7 100,000
3 45,000 8 106,000
4 63,000 9 108,000
5 78,000 10 107,000

a) Calculate the Marginal Product and find at what level of labor diminishing returns sets in

Ted is currently producing 100,000 bushels of hops per year for which he receives a price of $2 per bushel. Ted pays $10,000 per worker per year. Currently Ted does no work on the farm. He instead works as a stockbroker earning $50,000 per year. Being a stockbroker, he is aware of opportunities that would allow him to invest his money safely and earn 10%.

b) Find the economic profit per year for Ted’s farm at current production levels. How will this number look different than the accounting profit described by Ted’s bookkeeper?

c) Ted is worrying that the farm is not as profitable as he would like. He is decides to do some of the farm work he is currently paying for. He would no longer have time to do his work as a stockbroker but would still be aware of the same investment opportunities. If Ted has the same farming skills as a person he hires and wants to keep the same level of production, show what would happen to his accounting and economic profit with this decision Is this a good idea? Would it be a good idea if Ted was as productive as two workers?

1. In all these problems, the consumer is choosing to spend all hi...