Question

1. George needs to paint his living room walls. He could do it all himself, but would prefer to have some help. He is willing to pay someone up to $50 for the first hour of help, $45 for the second hour, $35 for the third hour, $20 for the fourth hour and $5 for the fifth hour. Assume the current price for painting services is $34 per hour:

   1. How many hours of painting services will George purchase?

   2. How much consumer surplus (if any) will George have as a result?

   3. How many hours will he purchase if the price drops to $25? What will be the change (if any) in consumer surplus relative to your answer to part (ii)? (Note: indicate the sign as well as the magnitude of the change.)

   4. Suppose, instead, that the price drops to $19? How many hours will he purchase? What will be the change (if any) in consumer surplus relative to your answer to part (ii)? (Note: indicate the sign as well as the magnitude of the change.)

Answer 1

1)

We can see that marginal willingness to pay for help is higher than current price of painting services till 3rd hour. but that marginal willingness to pay for help is lower than current price of painting services after 3rd hour. So, George will maximize net benefits by purchasing 3 hours of painting services.

2)

Consumer surplus is equal to sum of difference in willingness to pay and price for all quantities demanded.

Consumer surplus=(50-34)+(45-34)+(35-34)=$28

3)

If price drops to $25, we can see that there will not be any change in optimal number of painting services hired.

New Consumer surplus=(50-25)+(45-25)+(35-25)=$55

Change in CS=55-28=+$27

Consumer surplus is increased by $27

4)

If price drops to $19,

We can see that marginal willingness to pay for help is higher than current price of painting services till 4th hour. but that marginal willingness to pay for help is lower than current price of painting services after 4th hour. So, George will maximize net benefits by purchasing 4 hours of painting services.

New Consumer surplus=(50-19)+(45-19)+(35-19)+(20-19)=$74

Change in CS=74-28=+$46

Consumer surplus is increased by $46