Question

A simple economy has two goods, food (F) and soda (S) and two people, Jesse and Presly. The utility functions for Jesse and Presly are: Jesse’s utility function: UJ = 5F 0.5 S 0.5 (MUF = 2.5F-0.5S0.5 and MUS= 2.5F0.5S-0.5 ) Presly’s utility function: UP = 5F 0.75 S 0.25 (MUF = 3.75F-0.25S0.25 and MUS = 1.25F0.75S -0.75 )

a. Find the marginal rate of substitution for each person.

b. Current prices are PF = $12 and PS = $6. Both of them have the income of Y = $120. Find the proportions that Jesse and Presly consume F and S to achieve an efficient exchange equilibrium.

c. Find the utility maximizing quantities of F and S for Jesse and Presly.

d. Producers of F are currently supplying 30 units and producers of S are supplying 25 units. Is the market in a competitive equilibrium? Explain. If not, how will the markets adjust toward an equilibrium? Are the three efficiency conditions satisfied? Explain.

Answer 1

a)

For j0

For Pritha

b)

Y = 120

Budget equation of both

For efficient exchange eqn, both IC should be tangent

c)

For j0,

max Uj s.t 2F + S = 20

For pritha

max Up s.t 2F + S = 20

D)

Now,

Supply : F = 30 & S = 25

Demand  

Demand of both F & S < Supply

Market is not competitive equation.

To make it Eqn, & both should fall such that there will be 0 excess dd for F & S