Reference no: EM13862256

1. Quasimodo consumes earplugs and other things. His utility function for earplugs x and money to spend on other goods y is given by
u(x, y) = 100x - x^2/2 + y.

(a) What kind of utility function does Quasimodo have?

(b) If the price of x is p and price of money spend on other goods (y) is 1, then what is his inverse demand curve for earplugs?

(c) If the price of earplugs is $50, how many earplugs will he consume?

(d) If the price of earplugs is $80, how many earplugs will he consume?

(e) Suppose that Quasimodo has $4,000 in total to spend a month. What is his total utility for earplugs and money to spend on other things if the price of earplugs is $50?

(f ) What is his total utility for earplugs and other things if the price of earplugs is $80?

(g) Utility decreases by 1,050 when the price changes from $50 to $80. What is the change in (net) consumer's surplus when the price changes from $50 to $80?

2. The demand for kitty litter, in pounds, is D(p)=20 - p + m, where p is the price of kitty litter and m is income.

(a) What is the price elasticity of demand for kitty litter when p = 10 and m = 80?

(b) What is the income elasticity of demand for kitty litter when p = 10 and m = 0? When p = 10 and m = 90?

3. For each of the following demand curves, compute the inverse demand curve.

(a) D(p) = max{10 - 2p, 0}.

(b) D(p) = 100/√p.

(c) ln D(p) = 10 - 4p.

(d) ln D(p) = ln 20 - 2 ln p.

4. For each production function calculate marginal products (MP) and technical rate of substitution (TRS). Also state that the production function exhibits which returns to scale (IRS, CRS or DRS)?

i) y = x1 + 2x2.

ii) y = 50 x1 x2.

iii) y = x11/4 x23/4.

v) y= √(x_1+ 2x_2 )