Question

Decision Point: Crunching the Numbers (a)

Now that you've presented the theory behind this merger to your colleagues, you need to substantiate that theory with numbers. So, let's see what your current numbers look like.

To begin, assume the following:

1. TG Taters has a constant marginal cost of production of $12 per ton, or MC_P = 12. For simplicity, assume that TG Taters has no fixed cost, so TG Taters ATC = MC_P = 12.
2. Fryworks has a constant marginal cost of distribution of $8 per ton, or MC_D = 8. For simplicity, also assume that Fryworks has no fixed cost, so Fryworks' ATC = MC_D = 8.
3. The retail demand per hour for the fries (Fryworks’ demand) is Q = 50 – 0.5P so that the inverse demand, which expresses P as a function of Q, is P = 100 – 2Q, in which Q equals the number of tons of waffle fries.  

Using this information, what is TG Taters' wholesale derived demand per hour?

Type values into the equation below, and click Submit.​​​

​P_w = blank − ​blank Q

Answer 1

The inverse retail demand function of fries faced by Frywork is given as P=100-2Q where P and Q denote the price of the fries and the quantity or the number of tons of the fries and the marginal cost and average total cost of Frywork are 8 or MC(D)=ATC=8. Now, based on the profit-maximizing condition or principle of any competitive firm, any firm would produce the output which corresponds to the equality between the marginal cost of production and the price of the concerned product/good or service.

Therefore, based on the profit-maximizing condition or principle of any competitive firm, it can be stated:-

P=MC(D)

100-2Q=8

-2Q=-100+8

-2Q=-92

Q=-92/-2

Q*=46

Hence, the profit-maximizing amount of the fires for Frywork is 46 tons

Now, plugging the Q* into the inverse demand function of Frywork, we get:-

P=100-2Q

P=100-2*(46)

P=100-92

P=8

Thus, the profit-maximizing price charged by Frywork for distributing fries would be 8.

Now, the marginal cost and average total cost of TG Waters are both 12 or MC(P)=ATC=12

Again, based on the profit-maximizing principle or condition of any competitive firm, we can state here:-

P=MC(P)

100-2Q=12

-2Q=-100+12

-2Q=-88

Q=-88/-2

Q*=44

Therefore, the profit-maximizing retail quantity or amount of fries that TG Waters is willing to sell is 44 tons per hour.

Now, plugging the value of Q* into the inverse demand function, we get:-

P=100-2Q

P=100-2*(44)

P=100-88

P*=12

Hence, the profit-maximizing retail price of the fries charged by TG Waters would be 12.