The blue curve in the following calculator represents the demand curve facing a

Question

The blue curve in the following calculator represents the demand curve facing a firm. Use the calculator to help you answer the following questions Tool tip: Use your mouse to drag the green line on the graph. The values in the boxes on the right side of the calculator will change accordingly. You can also directly change the values in the boxes with the white background by clicking in the box and typing. The graph and any related values will change accordingly. CALCULATOR PRICE 100 Quantity Number of units produced Demand Price Dollars per unit) 80 50 60 20 20 40 60 80 100 QUANTITY (Units per day On the calculator, slide the green line along the curve to see what price this firm can sell its product for if it produces o, 20, 40, 50, 60, 80, or 100 units. Calculate the total revenue (price times quantity) for each of these production levels, and plot the results on the following graph using the blue points (circle symbol). Line segments wil automatically connect the points. Remember to plot from left to right. After you're finished, put y each of the points you've plotted (without clicking) to make sure they're in exactly the right spot. our mouse over TOTAL REVENUE (Dollars per dayl 2600 2275 Total Revenue 1950

Explanation / Answer

First Identify the Demand Equation

At P=100,Q=0 suppose the Equation is P=mQ+100 Now at P=0 Q=100 this gives Equation to be P=-Q+100

so at

So Now if Q=40 and Output is increased by a monopolist the quantity effect will dominate since Quantity is lower than the quantity at equilibrium for Maximum Revenue and hence total revenue will Rise

Total revenue at

Marginal Revenue of 20th Unit is Total revenue of 20 units- Total revenue of 19 unit=1600-1539=$61

Marginal Revenue of 40th Unit Produce is Total revenue of 40 units-Total revenue of 39 units=2400-2379=$21

Revenue Equation is (100-Q)*Q=100Q-Q2=R

Marginal Revenue =dR/dQ=100-2Q hence, at Q=50 Marginal revenue=0

and Graph for Revenue will maximize at Q=50 wher marginal revenue=0

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