1. The demand for a new drug is given by P = 4 – 0.5Q. The marginal cost of manufacturing the drug is constant and equal to $1 per unit. (Prices and costs are in terms of dollars, and quantities are in millions).
a. Illustrate on a diagram the following curves: demand, marginal cost, and marginal revenue.
b. If the firm receives a monopoly patent, what price does it charge and how much does it sell? Compute the firm’s surplus (profit) from selling the drug, not including fixed costs.
c. Suppose the fixed cost of developing the new drug is $6.5 million. Will the firm want to invest in developing the drug? Is the firm’s decision socially efficient?
a. To illustrate the demand, marginal cost, and marginal revenue curves, we can first start by plotting the demand curve. The demand equation is given as P = 4 - 0.5Q.
To plot the demand curve, we need to assign values to the quantity Q and calculate the corresponding prices P. Let's choose a range of values for Q, such as 0, 1, 2, 3, 4, and 5:
Q | P
--------------
0 | 4
1 | 3.5
2 | 3
3 | 2.5
4 | 2
5 | 1.5
Plotting these points on a graph, we can draw a downward-sloping line to represent the demand curve. The curve will start at P = 4 on the vertical axis and intersect the horizontal axis at Q = 8.
Next, let's plot the constant marginal cost of $1 per unit. Since marginal cost is constant, we can draw a horizontal line at P=$1 above the horizontal axis.
Finally, we can plot the marginal revenue curve. Recall that marginal revenue (MR) is the additional revenue generated by selling one more unit of the product. In a monopoly setting, MR is equal to the price of the product (P). Hence, the marginal revenue curve will coincide with the demand curve.
b. If the firm receives a monopoly patent, it can set the price and quantity it wants to sell. To find the equilibrium price and quantity, we equate the marginal cost (MC) with the marginal revenue (MR), which is equal to the price (P).
Since the marginal cost is constant at $1, we can set MC = MR = P = 1.
Substituting this into the demand equation, we get:
1 = 4 - 0.5Q
Rearranging the equation to solve for Q:
0.5Q = 4 - 1
0.5Q = 3
Q = 3 / 0.5
Q = 6
Therefore, the firm will sell 6 million units of the drug at a price of $1 per unit.
To calculate the firm's surplus/profit, we need to subtract the total cost from the total revenue. The total revenue is given by the price multiplied by the quantity sold:
Total revenue = Price x Quantity = $1 x 6 million = $6 million
The total cost includes the fixed cost of developing the drug ($6.5 million) and the variable cost, which is the cost per unit multiplied by the quantity sold:
Total cost = Fixed cost + (Variable cost per unit x Quantity)
Total cost = $6.5 million + ($1 x 6 million) = $6.5 million + $6 million = $12.5 million
The firm's surplus or profit is calculated as the difference between total revenue and total cost:
Surplus = Total revenue - Total cost
Surplus = $6 million - $12.5 million = -$6.5 million
The firm incurs a loss of $6.5 million from selling the drug, not including fixed costs.
c. To determine if the firm will want to invest in developing the drug, we need to compare the total revenue and total cost of developing the drug.
The total cost of developing the drug is given as $6.5 million.
To calculate the total revenue, we need to find the price and quantity at which the drug will be sold. From part b, we know that the firm will sell 6 million units at a price of $1 per unit.
Total revenue = Price x Quantity = $1 x 6 million = $6 million
The firm is incurring a total cost of $6.5 million to develop the drug but will only generate total revenue of $6 million. Therefore, the firm will not want to invest in developing the drug because it will result in a loss.
From a social efficiency perspective, we need to consider if the society as a whole benefits from the development of the drug. If the drug provides significant benefits to the society, it might be considered socially efficient, even if the firm incurs a loss. However, without further information on the benefits of the drug, we cannot determine if the firm's decision is socially efficient.