Question

Assume that at a price of $2.00 per pound, the annual supply of coffee beans in Country A is 8 million pounds, while the demand is 10 million pounds. At a price of $3.00 per pound, the supply is 10.2 million pounds, and the demand is 8.6 million pounds. Assume that the price-supply and price-demand equations are linear.

1. Write an equation for each (price on the y-axis)

2. Find the equilibrium point (point of interception of the two linear equations)

3. Discuss the significance of the equilibrium point in this case

4. Graph the two equations in the same Cartesian system (upload)

Answer 1

1. Let the supply equation be S = a+bp, where p is the price per pound of coffee beans , S is the annual supply of coffee beans in the country A and a,b are arbitrary real numbers.

Since at a price of $2.00 per pound, the annual supply of coffee beans in Country A is 8 million pounds, hence 8 = a+2b…(1). Also, since at a price of $3.00 per pound, the annual supply of coffee beans in Country A is 10.2 million pounds, hence10.2 = a+3b…(2). On solving these equations, we get a = 18/5 = 3.6 and b = 11/5 = 2.2 so that S = 3.6+2.2p.

Now, let the demand equation be D = c-dp where c,d are arbitrary real numbers and D is the annual demand of coffee beans in the country A.

Since, at a price of $2.00 per pound, the annual demand of coffee beans in Country A is 10 million pounds, hence 10 = c-2d…(3). Also, since at a price of $3.00 per pound, the annual demand of coffee beans in Country A is 8.6 million pounds, hence 8.6 = c-3p…(4). On solving these equations, we get c = 64/5 = 12.8 and d =7/5 = 1.4. Hence D = 12.8- 1.4p .

2. If S = D, then 3.6+2.2p = 12.8-1.4p or, (2.2+1.4)p = 12.8-3.6 or, 3.6p = 9.2 so that p = 2.56 ( on rounding off to 2 decimal places). Thus, the equilibriumprice of coffee beans in country A is $ 2.56 per pound.

3. At the equilibrium price, the annual supply of the coffee beans in Country A will equal the annual demand.

4. A graph of the supply equation (in red) and the demand equation (in blue) is attached.