Question

# 1. Suppose utility is given by U=√x+√y (where x and y denote

quantities), the prices of goods x and y are Px=Py=1, and income I=12.

The optimal bundle has what quantity of x?

The optimal bundle has what quantity of y?

2. Good x undergoes a price shock, and now Px=2.

The new optimal bundle has what quantity of x?

The new optimal bundle has what quantity of y?

3. Consider the optimal bundle after applying the substitution effect, but before applying the income effect.

The optimal bundle after the substitution effect has what quantity of x?

The optimal bundle after the substitution effect has what quantity of y?

4. Mark likes to eat pizzas and watch TV. In order to buy pizzas, he is looking for a job that pays him a wage of $w per hour for L hours of labor. Since he can only work a maximum of 15 hours a day (Mark needs 9 hours of sleep to function) and he cannot watch TV while working, he needs to decide how to allocate his time between working and watching TV during the time when he is awake, which is always a tough decision. Specifically, Mark's utility from pizzas and TV is:

U(P,T)=2ln(P)+ln(T)

where P is the number of pizzas and T is the number of hours he spends on TV. (Assume both P and T are infinitely divisible.)

Suppose a pizza costs 10 dollars. What will be Mark's daily budget constraint over pizzas and TV as a function of P, T, and w?

a. 10P+15w+wT=0

b. 10P+10w=wL+5w

c. None of these options

d. 10P+wT=15

e. 10P+15w=wT