if Q = 60 − (1/2)P, and MC = 60, which means that MR = 60 how do you work out the price, which then allows you to work out the Q.

does the graph still exhibit a slope at twice the rate of the demand curve?

thanks for looking in

To determine the price and quantity, we can start by rearranging the equation Q = 60 - (1/2)P to solve for P.

Q = 60 - (1/2)P
Add (1/2)P to both sides:
(1/2)P + Q = 60
Subtract Q from both sides:
(1/2)P = 60 - Q
Multiply both sides by 2 to get rid of the fraction:
P = 2(60 - Q)
P = 120 - 2Q

Now we have the price equation in terms of quantity. Since the marginal cost (MC) is constant at 60, and marginal revenue (MR) is also 60, we can set MR equal to MC to find the equilibrium quantity.

MR = MC
60 = 120 - 2Q
Rearranging the equation:
2Q = 120 - 60
2Q = 60
Divide both sides by 2:
Q = 30

Now that we have the equilibrium quantity, we can substitute it back into the price equation to find the price:

P = 120 - 2Q
P = 120 - 2(30)
P = 120 - 60
P = 60

Therefore, at equilibrium, the price is 60 and the quantity is 30.

Regarding the question about the slope of the graph, the demand curve usually exhibits a negative slope, meaning that as the price increases, the quantity demanded decreases. If the marginal revenue (MR) is equal to the marginal cost (MC), it means that the slope of the demand curve and the supply curve is the same in this case. However, without additional information, we cannot determine if the slope remains the same or changes for the given scenario.