Table HW8-1 Quantity | Total Revenue | Total Cost 0 | $0 | $10 1 | 9 | 14 2 | 18 | 19 3 | 27 | 25 4 | 36 | 32 5 | 45 | 40 6 | 54 | 49 7 | 63 | 59 8 | 72 | 70 9 | 81 | 82 Refer to Table HW8-1. What is the equilibrium price in this market? $6 $7 $8 $9
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In other words, it's the price at which the total revenue equals the total cost. Looking at the table, we can see that the total revenue equals the total cost at a quantity of 8. The total revenue and total cost at this quantity are both $72. Show more…
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Key Concepts
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Consider total cost and total revenue given in the following table: $$\mathrm{Quantity} \quad 0\quad 1\quad 2\quad 3\quad 4\quad 5\quad 6\quad 7 $$ $$\mathrm{Total cost} \quad$8\quad 9\quad 10\quad 11\quad 13\quad 19\quad 27\quad 37 $$ $$\mathrm{Total revenue}\quad $0\quad 8\quad 16\quad 24\quad 32\quad 40\quad 48\quad 56 $$ a. Calculate profit for each quantity. How much should the firm produce to maximize profit? b. Calculate marginal revenue and marginal cost for each quantity. Graph them. ($Hint$: Put the points between whole numbers. For example, the marginal cost between 2 and 3 should be graphed at 2 $1\over2$.) At what quantity do these curves cross? How does this relate to your answer to part (a)? c. Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industry is in a long-run equilibrium?
Supply and demand data are in Tables 6.2 and 6.3 (a) Which table shows supply and which shows demand? (b) Estimate the equilibrium price and quantity. (c) Estimate the consumer and producer surplus. Table 6.2 $$\begin{array}{c|ccccccc} \hline q \text { (quantity) } & 0 & 100 & 200 & 300 & 400 & 500 & 600 \\ \hline p \text { (S/unit) } & 60 & 50 & 41 & 32 & 25 & 20 & 17 \\ \hline \end{array}$$ Table 6.3 $$\begin{array}{r|rrrrrrr} \hline q \text { (quantity) } & 0 & 100 & 200 & 300 & 400 & 500 & 600 \\ \hline p \text { (S/unit) } & 10 & 14 & 18 & 22 & 25 & 28 & 34 \\ \hline \end{array}$$
Antiderivatives and Applications
Application: Consumer and Producer Surplus
The following tables give price-demand and price-supply data for the sale of soybeans at a grain market, where $x$ is the number of bushels of soybeans (in thousands of bushels) and $p$ is the price per bushel (in dollars): $$ \begin{array}{cccc} \hline \multicolumn{2}{c} {\text { Price-Demand }} & \multicolumn{2}{c} {\text { Price-Supply }} \\ x & p=D(x) & x & p=S(x) \\ 0 & 6.70 & 0 & 6.43 \\ 10 & 6.59 & 10 & 6.45 \\ 20 & 6.52 & 20 & 6.48 \\ 30 & 6.47 & 30 & 6.53 \\ 40 & 6.45 & 40 & 6.62 \\ \hline \end{array} $$ Use quadratic regression to model the price-demand data and linear regression to model the price-supply data. (A) Find the equilibrium quantity (to three decimal places) and equilibrium price (to the nearest cent). (B) Use a numerical integration routine to find the consumers' surplus and producers' surplus at the equilibrium price level.
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Applications in Business and Economics
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