Answer to Question #168522 in Microeconomics for kelvin maina

Question

Question 2

Peter likes pork Ribs (R) and Chicken wings (C). His utility function is U(R, C) = R

1/2C. His 

weekly income is $90 which he spends exclusively on R and C. The price for a slab of ribs is $10 

and $5 for a piece of chicken. 

Required:

a)

State Peter’s consumer problem 

b)

Determine Peter’s optimal consumption bundle? 

c)

Determine Peter’s demand function for ribs? 

d)

Are ribs a normal or inferior good? Explain.

 

e)

The price of ribs falls to $5. Using an appropriate diagram, show the income and 

substitution effects of this price change.

 

f)

Use the Langragian Multiplier method to determine Peter’s optimal bundle if his

utility function was given by U= √R+√C? Assume the price for a slab of ribs is $10 

and $5 for chicken and a level of income equal to $100. 

g)

Differentiate between the Marshallian and the Hicksian demand functions 

Answer 1

$$Solution$$

a. Peter wants to choose the bundle $(R,C)$ that maximizes her utility subject to the budget constraint.

$Max_{R,C}(R^\frac{1}{2}C) \ S.t\ 90 \ge10R+5C$

b. The U-function is of the Cobb-Douglas type, we know that the ICS are 'nice and convex'; Hence the optimum bundle satisfies the slope condition and is also on the budget line.

Slope condition$\frac{MU_R}{MU_C}=\frac{P_R}{P_C}\implies\frac{2C}{R}=2\\$

Budget line $90=10R+5C\implies10R+5R=90\implies15R=90R^*=6,C^*=6$

$c.\frac{2C}{R}=\frac{P_R}{5}\implies\ C=\frac{P_RP}{10}\\ 90=P_R+5\frac{P_RR}{10}\implies\ P_RR+\frac{1}{2}P_RR=90\implies\frac{3}{2}P_RR=90\implies\ R(P_R)=\frac{60}{P_R}$

d. Normal, this is because demand increases as income increases

e.

$f. MRS=\frac{\frac{1}{2}R-\frac{1}{2}}{\frac{1}{2}c-\frac{1}{2}}=\frac{C}{R}=4\implies\ c=4R\\ 90=10R+5(4R)\implies90=30R\implies\ R^*=3, C^*=12$

g. Marshallian demand curves simply show the relationship between the price of a good and the quantity demanded of it.

Hicksian demand curves show the relationship between the price of a good and the quantity demanded of it assuming that the prices of other goods and our level of utility remain constant.