Question

2 and 3 please.

A consumer purchases two goods, food (F) and clothing (C). Her utility function is given by U(F,C)= FC +F. The marginal utilities are MU, = C +1 and MUS = F. The price of food is Pc , the price of clothing is Pc, and the consumer's income is I. 1) What is the demand curve for clothing? 2) Is clothing a normal good in this case? Charlie consumes two goods, professional baseball games (B) and mystery novels (N). The price of baseball games is P,; the price of mystery novels is Py. Charlie has an income of I to spend on these two goods. Charlie's utility function can be represented as U = B²N, with MU, = 2BN and MU, = BP. 1) What is the demand curve for mystery novels? 2) What is the Engel curve for mystery novels? 3) Are mystery novels a normal good?

Answer 1

2)1)

MUf/pf=MUc/pc

(C+1)/pf=F/pc

Solve for F,

F=(C+1)*pc/pf

I=Pf*F+Pc+C

I=pf*(C+1)pc/pf+Pc*C

I=(C+1)*pc+pc*C=2pc*C+pc

I-pc=2pc*C

C=(I-pc)/2pc{ demand for clothing}

2)2) normal good have a positive relationship between Income and quantity demanded.

So we need to DERIVATIVE demand function with respect to Income and check if it is positive or not.

C=(I-pc)/2pc=I/2pc-0.5

DERIVATIVE of demand function with respect to I,

1/2pc

So DERIVATIVE is positive ,so the good is normal good.

3)1)MUb/pb=MUn/pn

2BN/pb=B^2/pn

Solve for B,

B=2N*Pn/pb

I=(2N*Pn/pb)*pb+pn*N

I=2N*pn+pn*N

I=3pn*N

N=I/3pn{ demand for mystery novels}

3)2) Engel curve shows the relationship between income and quantity demanded of a good.

DERIVATIVE of mystery novels demand with respect to I

1/3pn,

So positive DERIVATIVE tells goods is normal good ,so Increase in income leads to increase in quantity demanded.,so Engel curve for mystery novels will be upward sloping straight line.

3) yes, positive DERIVATIVE of demand of mystery novels tells there is positive relation between quantity demanded and income of consumer. So mystery novels are normal good