Explain in words and with a graph why a 15 cent per gallon

Question

1. When the price of cigars increases by 20%, customers buy about 5% fewer cigars.

a. What is the elasticity of demand for cigars?

b. Is demand at the current price elastic or inelastic?

c. If you are an importer of Cuban Cigars, would you like to raise or lower your prices? Why?

2. Are the following functions convex or concave?

a. y=2x²+10

b. y = x²+2x+1

c. y = x^0.5

d. y = 2x³+x²+1

e. y = abs(x)

3. Explain in words and with a graph why a 15 cent per gallon tax on milk could be collected from milk producers or from milk consumers at the store with the same result?

4. Consider the market for sunscreen. 

The demand for sunscreen is given by Q = 100 - 4p.

The supply for sunscreen is given by Q = 6p.

a. Find the efficient price and and quantity of sunscreen

b. At the equilibrium price and quantity find the elasticity of demand and the elasticity of supply.

c. Suppose the government opts to levy a per unity tax of 1.00 onto the sale of sunscreen. What is the new equilibrium price and quantity. How much of the tax are producers able to pass onto the consumer?

d. Due to climate change the demand for sunscreen has fundamentally shifted.  The new elasticity of demand is -0.0012.  If the supply function is unaffected, now how much of the $1 tax will now be passed along to consumers?

5. Ryan has the utility function U(Pizza, Robots) = 4(Pizza)^0.75(Robots)^0.25.

a. If the price of robots is 12 and the price of a pizza is 4, and Ryan's total income is 120. What is his optimal consumption bundle of pizza's and robots?

b. Suppose the price of robots increases to 18. What is the new optimal bundle?

c. Using your answers to a and b derive Ryan's likely demand curve for robots.

d. Using your answer to a and b and c derive an estimate of Ryan's elasticity of demand for robots.

e. Suppose Ryan's income is cut to 90. What is the new optimal bundle when the price if pizza is 4 and a robots is 12.

f.   What is Ryan's income elasticity of Robot demand?

g. What kind of good are Robots for Ryan?

6. For each of the following utility functions derive the Marginal Utility of X, the Marginal Utility of Y and the MRS for X and Y. In each case describe the relationship between X and Y?

a. U(X,Y) = X^a+Y^b

b. U(X,Y) = X^YYy

c. U(X,Y) = ln(X)-Y

d. U(X,Y) = min(X,Y)

7. Suppose demand is given by Q = 10p^0.5.  Is demand elasitic or inelastic at the optimal consumption bundle? Explain.