Question

Suppose you're analyzing the market for pancakes and sausage on a stick and the market is comprised of two firms. The first firm is Jimmy and jimmy has been in this market for years and has first-mover advantage. The brand GreatValue also decides that they will produce and sell pancakes and sausage on a stick. You know that the market demand for pancakes and sausage on a stick is P = 100 – Q. And you also know that the cost function for Jimmy Dean is C = 10Q and the cost function for Great Value is C = 20Q.

a) Calculate the equilibrium quantity produced by each firm when they maximize profits.

b. Calculate the profits of each firm.

Answer 1

We know that Total Revenue equals Price multiplied by Quantity.

Or  TR = Price (P) * Quantity (Q)

  In the given question, The market demand equation is given as follows -

P = 100 - Q

The TR can be found by using the above equation in TR = Price (P) * Quantity (Q)

TR = (100 - Q) * Q

Or TR = 100Q - Q2  

Differentiating w.r.t Q, we get

MR = 100 - Q

Now we know that profit is Maximised at a Quantity where Marginal Revenue equals Marginal Cost.

So, by taking the Marginal Cost function of both sellers we can calculate the Quantity of each seller.

For Jimmy Dean the cost function is given as

C = 10Q  

Differentiating w.r.t. Q, we get

MC = 10

Jimmy Dean will maximize profit at a point where Marginal Revenue equals Marginal Cost.

Therefore,

100 - Q = 10

Or Q = 90

Therefore, the quantity comes out to be 90 units.

- Quantity is 90 units for Jimmy Dean.

Now the same steps can be applied to calculate the Quantity for Great Value whose Marginal Cost function is calculated as MC = 20

So,

100 - Q = 20   ( As MR equals MC where profit is maximised)

Or Q = 80

Therefore the Quantity for Great Value is 80 units.

Now we can use the above calculations to answer the question on equilibrium quantity.

(a) For Jimmy Dean the profit will be maximized at Q = 90 units.

And for Great Value profit will be maximized at Q = 80 units.

(b) Profit = Revenue - Cost

For Jimmy Dean the Cost function is C = 10Q and the Total Revenue function is TR = 100Q - Q2  

The quantity was calculated 90 units for Jimmy Dean and the same can be substituted in the Market demand function to obtain the price.

So,

P = 100 - Q (given )

P = 100 - 90 (substituting Q value)

P = 10

Now, the Total Revenue for Jimmy Dean can be calculated as follows -

TR = P* Q

TR = 10* 90

TR = 900

And Cost = 10* 90 ( substituting Q value in Cost function)

C = 900

Profit = R - C

Profit = 900 - 900 = 0

Therefore, Jimmy Dean obtains no profit.

For Great Value cost function is C = 20Q and quantity is 80 units.

By substituting quantity in the cost function, we get,

C = 20 * 80

C =1600

ANd by substituting the quantity value in the Market Demand function, we get

P = 100 - 80 ( Quanity value for Great Value is 80)

P = 20

Now, TR = P* Q

TR = 20* 80

TR = 1600

Profit = TR - TC

Profit = 1600 - 1600 = 0

Therefore, for Great Value as well there will be no profits.