True or false with explanations please

1.All ordinary goods are also normal goods.

2. If demand is elastic at the current quantity sold, then an increase in quantity sold will result in an increase in total revenue.

3. A quantitysubsidyof $1 per unit sold in a market would result in an increase in the equilibrium quantity bought/sold.

4. The substitution e ect of a price change always makes the consumer increase their quantity demanded.

5. The production functiony=x1=3x3=4has increasing returns to scale for any positivex121

andx2.

Problem 1

J the consumer consumes only two goods with quantitiesx1andx2respectively. J's utility

function is:u(x1;x2) = lnx1+x2+2. Let the prices bep1= 1; p2= 6 and J's income bem= 60:

(a) What are J's optimal quantities demanded of each good? Graph his budget line and label his optimal bundle asA.(Hint: You may want to derive J's optimal quantities demanded for anyp1; p2; mand then just plug in the given values)

Suppose now that the government puts a quantity tax that increases the price of good 1 top01= 2.

(b) What are J's optimal quantities demanded of each good after the tax is imposed? Plot his new budget line on the graph from (a) and denote his optimal bundle byC.

(c) To how much must J's income be adjusted after the tax is imposed so that he can just a ord his optimal bundle from (a)?

(d) What would J's optimal quantities demanded for each good be with the adjusted income as in (c) at the after-tax prices. Plot the budget line corresponding to this bundle on your graph and denote the optimal bundle byB.

(e) Given your results nd the income and substitution e ects of the change inp1on J's consumption of each good. Explain brie y the intuition for the results.

Problem 2

The market demand function for computer games isqD(p) = 3006pand the market supply function isqS(p) = 4p:

(a) Find the equations of (express price in terms of quantity) and plot the demand and supply curves corresponding to the given market demand and supply functions. Find the market equilibrium price and quantitypandq.

(b) Find the producer's surplus and consumer's surplus at the equilibrium.

(c) What is the price elasticity of demand at the equilibrium point?

(d) Derive the equation of the marginal revenue curve and compute the marginal revenue

at the equilibrium point in (a).

(e) Given the demand function, at what price would total revenue be maximized?

(f) Suppose a quantity tax of $5 per game is imposed on the computer game suppliers.

What is the new equilibrium price paid by the consumers? What is the new equilibrium price received by producers? How much is the tax revenue? How much is the deadweight loss of the tax? Use a graph to explain your answers.

Problem 3

Suppose the production function of a rm is given byf(K;L) = 8K1=4L1=2, whereKis capital andLis labor.

(a) Find the expressions for the marginal product of capital and the marginal product of labor.

(b) Write down the equation of the isoquant corresponding to an output level of 10. (c) What is the technical rate of substitution (TRS) atK= 10 andL= 20?