Question

5. Paul’s utility from watching movies (M) and eating popcorns (P) is:

   U=M4P1/2

We know that the price of one movie ticket is $12 and the price of one tub of popcorn is $6. He plans to spend no more than $24 on movies and popcorns. What is the consumption bundle that maximizes his utility when he goes to see one movie? What is his utility at this bundle?

Answer 1

Given

U=M⁴P^1/2

Price of one movie ticket=Pm=$12

Price of a tub of pop corn=Pp=$6

Maximum amount than can be spent=C=$24

Expenditure limit is given by

C=MPm+P*Pp

24=12M+6P ----------------(1)

Marginal Utility from Movies (MUm)=dU/dM=4M³P^1/2

Marginal Utility from Popcorn (MUp)=dU/dP=(1/2)M⁴P^-1/2

In case of utility maximization, we know

MUm/MUp=Pm/Pp

(4M³P^1/2)/(1/2)M⁴P^-1/2=12/6

8P/M=2

M=4P

So, Put M=1

1=4P

P=0.25

Optimal combination is 1M and 0.25 P

Expenditure at this consumption=1*12+0.25*6=$13.50

Paul still has the money to spend. Marginal utility of popcorn per dollar spend will be less as compared to marginal utility per dollar spent in case of movie. But total utility will increase, So, Paul can increase the consumption of popcorn to maximize the utility.

So,

24=12*1+6*P

P=2

Paul should consume 2 units of popcorn to maximize the utility while going for one movie.

We are given

U=M⁴P^1/2

Put M=1 and P=2

U=(1)⁴*(2)^1/2=1.414 utils