Problem 1:

Luke likes to consumer CDs (good1) and pizzas (good 2). His preference over both goods is given by the utility function

If Luke allocates $200 to spend on both goods and if a case of CDs costs $20 and a pizza costs $10, how many cases of CDs and pizzas would he consume in order to maximize his utility subject to his income. Show your work and illustrate your answer graphically.

Problem 2:

Consider Garfieldís utility function given as

where x₁ is lasagna and x₂ is "everything else". Suppose his allowance from Jon is m = $8 and p₁ = $1 and p₂ = $1

(i) Find Garfieldís optimal choice of lasagna and everything else and illustrate your answer graphically. Show your work.

(ii) Find an expression of Garfieldís marginal rate of substitution between lasagna and all other goods and explain its meaning at the initial choice that you found in (i).

(iii) If the price of lasagna doubled, i.e., p₁ increased from p₁ = $1 to p'₁= $2, what would be Garfieldís new optimal bundle? Show the bundle on your graph.

(iv) Under the assumption that Garfieldís demand for lasagna is linear, derive the demand equation from his two optimal bundles computed in (i) and (iii). Illustrate your answer graphically by drawing two graphs: one representing Garphieldís optimal choice and the other representing his demand curve for lasagna driven from the two optimal bundles.

(v) Compute Garfieldís price elasticity of demand for lasagna between the two prices p₁ = $1 and p'₁ = $2 and explain its meaning.
(vi) Compute Garfieldís price elasticity of demand at p₁ = $3:
(vii) If Garfield always consumes lasagna with garlic bread. Show the effect of an increase in the price of wheat on (a) the wheat market, (b) the bread market, and (c) the market for lasagna. Draw three graphs to illustrate your answer (one graph for each market).

Problem 3: Elasticity, Total Revenue and Marginal Revenue

For Each of the following cases, what is the expected impact on the total revenue of the firm? Explain your reasoning

(a) Price elasticity of demand is known to be 0:5 and the firm raises price by 10%.
(b) Price elasticity of demand is known to be 2:5 and the firm lowers price by 5%.
(c) Price elasticity of demand is known to be 1:0 and the firm raises price by 1%.

Problem 4

Suppose the demand equation for good x was estimated as

(a) What is the price at which total revenue is maximized and what is the value of the total revenue at this point. Illustrate graphically.

(b) Identify the elastic and the inelastic ranges on the demand curve.

Problem 5: Effect of changing supply on total revenue

Farm stories for July 26th, 2007. Written by Jim Birchard, Bayshore Broadcasting Corp. The largest winter wheat crop ever produced in Western Canada is set to begin harvesting this week. The Canadian Wheat Board says the 1.45 million acres seeded to the crop will yield record production. Winter-wheat yields are on track to match or surpass last yearís record-setting yield results.

Based on the above excerpt, would you expect the income of the wheat farmers to increase or decrease? Explain with a demand-supply diagram.

Problem 6: Movements Versus Shifts

For each of the following statements, determine whether there has been a change in supply or change in quantity supplied. Draw a demand and supply diagram for each situation to show either a movement along the supply curve or a shift of the supply curve.

(a) The price of Canadian-grown peaches skyrockets during an unusually cold summer that reduces the size of the peach harvest.

(b) An increase in income leads to an increase in the price of beef and also to an increase beef sales.

(c) Technological improvements in the microchip lead to price reductions for personal computers and an increase in computer sales.

(d) Greater awareness of the health risks from smoking lead to a reduction in the price of cigarettes and to fewer cigarettes being sold.

Problem 7

Because bagels and cream cheese are often eaten together, they are complements.

(a) We observe that both the equilibrium price of cream cheese and the equilibrium quantity of bagels have risen. What could be responsible for this pattern - a fall in the price of flour or a fall in the price of milk? Illustrate and explain your answer.

(b) Suppose instead that the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen. What could be responsible for this pattern ña rise in the price of flour or a rise in the price of milk? Illustrate and explain your answer.