Question

1. You decide to set-up a lemonade stand outside AT&T Park before a Giant’s game. You conduct extensive market research and discover that if you charge $1 / glass, you will sell 10,000 glasses; if you charge $6 / glass, you will sell 5,000 glasses.

1. At the beginning of the season, you purchased all of the equipment you need (the stand, pitchers, mixers, etc.) for $500. This equipment has no resale value. You estimate that each glass of lemonade will require $0.01 of water, $0.02 in lemons and $0.02 of sugar. Since you would otherwise be sitting at home bored, your labor is costless. Just before you are ready to launch your venture, you discover that San Francisco charges a $12,000 license fee to set up your stand for the game. Write expressions for your total (economic) cost, average total cost and marginal cost as functions of Q.

2. Based on these functions, how many glasses will you produce and sell, what price will you charge and how much economic profit will you make?

3. You realize that if it rains, you will sell 4,000 fewer glasses at any given price. San Francisco has a 50% chance of rain on any given day. Unfortunately, you must decide whether to pay your license fee before you know whether it will rain. However, you can decide how many glasses of lemonade to produce after you have learned whether it will rain. Write the expression describing the demand curve during rain as a function of P.

4. Conditional on having paid the license fee, if it rains, how many glasses will you produce and sell, what price will you charge and how much profit will you make?
5. Should you pay the license fee and operate?
6. Suppose a meteorologist could tell you with 75% certainty whether it will rain BEFORE you have to pay your fee, how much would you be willing to pay for such a forecast?

Answer 1

a) Fixed cost= $500 +$12000= $12500

Let Q number of glasses of lemonade are produced.

The cost of producing 1 glass of lemodade= $( 0.01+0.02+0.02) =$0.05

the cost of producing Q glasses of lemonade= 0.05Q, this is the variable cost.

The total cost of the firm becomes

C= 12500+ 0.05Q

Average cost= C/Q= 12500/Q + 0.05

Marginal cost= 0.05

b) If the lemonade stand is under perfect competiton, then the price of oe glass of lemonade is equal to the marginal cost.

Thus, P= 0.05