Question

Microeconomics

1. (4 pts) Karen is currently donating monthly (12 times per year) to her favorite charity and is purchasing one meal per month (12 per year) at Olive Garden. She donates $20 per month to the charity and a meal costs her $12. At her current rate of contribution/consumption, her marginal utility for donations is 40 and her marginal utility for meals is 18. Is she maximizing her utility? If she is, explain why. If she is not, explain why not (show your math) and what do you recommend that she do to maximize her utility?

2. (10 pts) The Papa John’s recently did a price experiment for selling pizza and found the following price / quantity purchased relationships:

Price                                        Quantity Purchased

$8                                            62

$10                                          58

$12                                          41

1. Calculate the price elasticity of demand between $8 and $10. Is it elastic or inelastic? (You must show your work to receive credit for this question)
2. Calculate the price elasticity of demand between $10 and $12. Is it elastic or inelastic? (You must show your work to receive credit for this question)
3. Would you recommend raising the price from $8 to $10? Why or why not?
4. Would you recommend raising the price from $10 to $12? Why or why not?
5. In your opinion, what would be the ideal price? Explain why.

Answer 1

Answer 1)For Utility maximisation

(MU for donation/Price of donation)= (MU for meal/ Price of meal)

Given, MU of donation= 40 , Price of donation= 20 , MU of meal=18 , Price of meal = 12

So, (MU of donation/Price of donation)= 40/20 = 2

(MU of meal/ Price of meal)= 18/12= 1.5

Since, MU donation/Price of donation is greater than MU of meal/Price of meal , she is not maximizing utility,for utility maximisation they must be equal.

Now she should spend more on donation so that the law of diminishing marginal utility will work and satisfaction derived from additional donation will fall so that (MU donation/Price of donation) will fall and eventually will become equal to ( MU of meal/ Price of meal).

Answer 2 ) Price elasticity of demand = (P/Q)*(∆Q/∆P)

where P= original price, Q = Original quantity , ∆Q= New quantity-Old Quantity, ∆P = New price- Old price

Answer 2a) P= 8 ,Q= 62 , ∆P= 10-8= 2 , ∆Q= 58-62= -4

Price elasticity of demand=(8/62)*(-4/2)

PRICE ELASTICITY OF DEMAND= -0.26

The demand is inelastic since price elasticity of demand is <1

Answer 2b) P=10 , ∆P= 12-10= 2 , Q= 58 , ∆Q= 41-58= -17

Price elasticity of demand= (10/58)*( -17/2)

​​​​​​Price elasticity of demand= -1.46

The demand is elastic since the coefficient of elasticity of demand is > 1.

Answer 2c) According to the total revenue approach of elasticity of demand if there exist a direct relationship between total revenue and price then the elasticity of demand is less than 1. And if there exist an inverse relationship between price and total revenue then price elasticity of demand is greater than 1

• Yes, since the elasticity of demand is 0.26 it is less than 1 , there exist a direct relationship between price and total revenue so, Raising the price will raise the Total Revenue,so we will recommend raising the price from 8 to 10

Answer 2d) No, we will not recommended raising the price from 10 to 12. This is because since the elasticity of demand is 1.46 it is greater than 1 and there exist an inverse relationship between price and total revenue

A rise in price will fall the total revenue.