DescriptionIntermediate Microeconomics

Instructor: Sandhya Patlolla

Assignment 2

1. The demand for pizzas in a large town is written as: Qd = 26 − 10 P + 5 Pb − PS + 10Y , where

Qd is the quantity demanded, P is the price of pizza, Pb is the price of burrito, PS is the price of

soft drinks sold in the pizza restaurants, and Y is personal income per month (in thousand dollars).

Suppose Pb = $4; PS = $1 and Y = 3 (in thousand dollars) (Don’t substitute income has 3000. Use

Y =3)

The supply of pizza is: Qs = 30 + 5 P − 15 Pinput

Where: P = price of pizza and Pinput = price of the inputs = $2

(i) Draw the demand curve.

(ii) On the same panel above, draw the supply curve.

(iii)Find the equilibrium price and quantity of pizza.

(iv) Calculate the effect of the change in price of burrito on the equilibrium price and quantity using

comparative statics.

(v) Calculate the effect of the change in in the price of soda on the equilibrium price and equilibrium

quantity using comparative statics.

(vi) Calculate the effect of the change in in the income on the equilibrium price and equilibrium

quantity using comparative statics.

(vii)

Calculate the effect of the change in the price of the input ( Pinput ) on the equilibrium price

and equilibrium quantity using comparative statics.

(viii)

Estimate the following elasticities and interpret the values.

(a)

Price elasticity of demand for pizza at the equilibrium.

(b)

Cross-price elasticity of demand between pizza and burrito at the equilibrium.

(c)

Cross-price elasticity of demand between pizza and soda at the equilibrium.

(d)

Income elasticity of demand for pizza at the equilibrium.

(e)

Price elasticity of supply of pizza at the equilibrium.

2. Consider the following demand and supply functions for a good: =

2

; =

Suppose = $27, and = $2.

(i) Find the equilibrium price and equilibrium quantity.

(ii) Calculate price elasticity of demand at the equilibrium and interpret the value.

2

(iii)Calculate price elasticity of supply at the equilibrium and interpret the value.

(iv) Calculate income elasticity of demand at the equilibrium and interpret the value.

3. Joseph has the utility function ( , ) = 10 2 , where F is the quantity of food he consumes per

week and H is the quantity of housing per week. Suppose the price of food is $10 and the price of

housing is $5, while Joseph has an income of $150/week. (use food on X-axis and housing on Yaxis)

a.

Write Joseph’s budget constraint.

b.

Calculate Joseph’s MRS as a function of the quantities F and H.

c.

Write out Joseph’s constrained optimization problem

c. Using the Lagrangian method, solve for Joseph’s optimal consumption bundle of food and

housing.

d. Now suppose that price of food has increased to $15. Using MRS and MRT relationship at the

optimal, calculate new consumption bundle of food and housing.

4. Consider Jen, a consumer with preferences ( , ) = 1/3 2/3, where H is the quantity of

housing and F is the quantity of food (per month). Suppose Jen has a stipend of $600/month which

she uses to purchase food at a price of $1/unit and housing at a price of $10/unit. (use food on Xaxis and housing on Y-axis) Compute Jen’s utility-maximizing bundle of goods.

5. Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of

vodka has four times the alcohol as a six-pack of beer. Assume that Tony only cares about the

total amount of alcohol in his basket. (Use vodka on X-axis and beer measured in six-pack on Yaxis)

a) Devise a utility function to represent these preferences.

b) What is his marginal rate of substitution of a bottle of vodka for six-packs of beer?

c) Suppose a bottle of vodka costs $45, a six-pack of beer costs $15 and Tony has $180 budget.

Write the budget constraint.

d) Solve Tony’s utility maximization problem and find out optimal combination?

6.

Suppose Sara does not like to consume apple pie by itself or vanilla ice-cream by itself. However,

she loves to consume 2 slices of apple pie with 3 scoops of vanilla ice-cream. (use apple pie on Xaxis and bread on Y-axis).

a) Devise a utility function to represent these preferences.

b) Suppose a slice of apple pie costs $2 and scoop vanilla ice-cream costs $1. If she has $35

budget to spend on these goods. Write the budget constraint.

c) Solve Sara’s utility maximization problem and find out optimal combination?

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