Question

For the supply equation below, x is the quantity supplied in units of 1000 and p is the unit price in dollars

p = 1/2x + 40; p = 48
(a) Sketch the supply curve.
(b) Determine the number of units of the commodity the supplier will make available in the market at the given unit price.

Answer 1

Answering the student's question, the supply curve based on the equation p = 1/2x + 40 can be sketched with a price axis (p) and quantity axis (x), and to find the units supplied at a price of $48, we solve the equation to get x = 16, which indicates that 16,000 units will be supplied.

Step-by-step explanation:

The student is asking about plotting a supply curve based on a given supply equation and determining the quantity of goods supplied at a specific price. Given the supply equation p = 1/2x + 40 and the price p = 48, we need to follow two steps:

• Sketching the supply curve: To sketch the curve, plot the supply equation on a graph with p (price) on the vertical axis and x (quantity) on the horizontal axis. The curve will have a slope of 1/2 and a vertical intercept at p = 40.
• Determining units supplied at a price of $48: To find the quantity supplied at p = 48, substitute p with 48 in the equation to get 48 = 1/2x + 40. Solving for x, we subtract 40 from both sides, resulting in 8 = 1/2x, and then multiply both sides by 2 to find x = 16. Thus, producers will supply 16,000 units (as x is in units of 1000) at a unit price of $48.