EC335 Chapter Notes - Chapter pg. 1-34: Delta Ii, Perfect Competition, Strategic Dominance

A small firm faces an inverse demand function of P = 100 - Q. Its total cost function is given by TC = .5Q2. (You should see right away that marginal revenue is thus MR = 100 - 2Q, and it also happens that marginal cost is just MC = Q. Both MR and MC are the first derivatives of total revenue and total cost. And a quick comment on MC: unlike some marginal cost functions we've seen, this one is not constant, because marginal cost is getting $1 higher with each additional unit of output.)

The Chief Executive Officer will manage the firm, choosing output and price. Currently, the CEO is negotiating an incentive-based contract with the shareholders of the company.
(Hint: basing compensation on revenue will motivate revenue maximization rather than profit maximization!)

Hint: since the plan creates incentives for the CEO to maximize revenue rather than profit, you should not set MR = MC at this point. BIG hint: revenue is maximized when selling an additional unit won't increase your revenue, or in math terms, when MR = 0.)

Owners' proposal: CEO keeps 10% of TR.

I am having a tough time with this homework question. Please try to show work if possible! Thank you!

Garden of Edam sells fondue kits over the internet. The demand function for this product is Q = 20 - (1/3)P, where Q is the number of kits sold per week and P is the price per kit.

1. Solve for the inverse demand function. __I think it would be P=-60-(1/3)Q but correct me if I'm wrong please! Thanks!__________

2. What is the slope of this relationship in the standard P/Q diagram? ______________

3. Compute the point price elasticity of demand (PED) when

Q = 20 ________________ Q = 6 _________________

4. Compute the point PED when P = 30 __________ and P = 60 _____________.

5. Give a one sentence quantitative interpretation of the Q = 6 elasticity.

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6. Give a one sentence qualitative interpretation of the Q = 6 elasticity.

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7. Write the equation showing kit total

revenue (TR) as a function of Q. ___________________________________

8. Write the equation showing marginal revenue

(MR) as a function of Q. ___________________________

Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.

1. Find the marginal revenue MR1 of firm 1 as a function of q_1 and q_2.

2. Setting MR1=MC1, determine the reaction function of firm 1.

3. Find the marginal revenue MR2 of firm 2 as a function of q_1 and q_2.

4. Setting MR2=MC2, determine the reaction function of firm 2.

5. What quantity of output will each firm produce? That is, use the two reactions functions to find q_1 and q_2.

6. What is the market price P.

7. Determine the profits of each firm assuming there are no fixed costs.