Question

There is a fixed amount of coal (Q) available that can be consumed in period 1(q1) and/or period 2 (q2). The demand function for coal in each period is the same and is given by q1=200−p1q2=200−p2 ​Q=q1+q2 where p1 and p2 ​are the prices for coal in each period. Assume that the marginal extraction cost is zero. a. Calculate the equilibrium price and quantity in each period assuming that Q=169, the discount (interest) rate used by coal suppliers is 10% per.year, and coal suppliers are price takers (behaves competitively)

Answer 1

To calculate the equilibrium price and quantity in each period, we can start by finding the market demand and supply curves. By substituting the demand equations and solving, we find that the equilibrium price in each period is $115.5 with a total quantity of 169.

Step-by-step explanation:

To calculate the equilibrium price and quantity in each period, we can start by finding the market demand and supply curves. The demand function is q1 = 200 - p1 and q2 = 200 - p2, while the supply function is Q = q1 + q2. Since the suppliers are price takers, the price will be determined by the intersection of the demand and supply curves. Using the given information, we can substitute the demand equations into the supply equation and solve for the equilibrium price and quantity.

By substituting the demand equations, we have Q = (200 - p1) + (200 - p2) = 400 - (p1 + p2). Equating this with Q = 169, we can solve for p1 + p2 = 400 - 169 = 231. Since the suppliers are price takers, we can assume they will each take half of the total market for coal consumption. Therefore, p1 = p2 = 231/2 = 115.5. The equilibrium price in each period is $115.5 with a total quantity of 169.