//LabCalculateMRSpecs.swift. 2/4/2020. import Foundation class LabCalculateMRSpecs { let strMarRevCalSpecs :String = """ `` Lab Specs // Slider specs 0 800 50 400 // 0: Demand curve price intercept -.30 -.01 .01 -.02 // 1: Demand curve slope // Number of firms 1 2 5 10 100 500 1000 // 2: Number of firm vector Quantity_(Q) Price_(P) // 3: Axis names `` Prob Specs ` Problem 0 Start Screen 1 - Marginal Revenue Calculations // 0: Title // Slider visibility N L B L // 1: Demand intercept, Demand slope, // Firm Quantity, Number of firms // Effects visibility F // 2: Quantity and price effects visibility // Initial firm quantity 6000.0 // 3: Initial total quantity ` Text Start // 4: Text `RED`BLDObjective:`BLD show that the lab's calculations are correct.`BLK Note that there is only one firm in the market; that is, a monopoly exists. Also, the slope of the demand curve equals -.02. Initially, the monopoly's output is 6,000 and the price is $280.00. The table reports that when the monopoly sells 6,000 units the the monopoly's total revenue equals $1,680,000.00. Confirm that the table is reporting the correct value for total revenue. The table also includes a row for 6,001 units. Explain why the price must fall by $.02 from $280.00 to $279.80, in order for the monopoly to sell 6,001 units. Confirm that total revenue equals $1,680,159.98 and that marginal revenue equals $159.98 when the monopoly sells 6,001 units. Adjust the firm quantity slider to increase its output from 6,000 to 8,000. Confirm that the results reported on the table are correct. ` Prob End ` Problem 1 Start Screen 2 - Monopoly's Marginal Revenue and the Price Elasticity of Demand // 0: Title // Slider visibility N L B L // 1: Demand intercept, Demand slope, // Firm Quantity, Number of firms // Effects visibility F // 2: Quantity and price effects visibility // Initial firm quantity 6000.0 // 3: Initial total quantity ` Text Start // 4: Text `RED`BLDObjective:`BLD Show that a monopoly's marginal revenue is related to the price elasticity of demand. More specifically, show that marginal revenue is: `0x2022 positive when demand is elastic. `0x2022 negative when demand is inelastic.`BLK Recall that the price elasticity of demand varies along a linear demand curve: `0x2022 the upper half is elastic. `0x2022 the lower half is inelastic. Use the Firm's Quantity scrollbar to move along the demand curve. Is a monopoly's marginal revenue positive or negative when it operates in the demand curve's `0x2022 upper half, the elastic region? `0x2022 lower half, the inelastic region? In each case explain. ` Prob End ` Problem 2 Start Screen 3 - Monopoly's Price and Output Effects // 0: Title // Slider visibility N L B L // 1: Demand intercept, Demand slope, // Firm Quantity, Number of firms // Effects visibility F // 2: Quantity and price effects visibility // Initial firm quantity 6000.0 // 3: Initial total quantity ` Text Start // 4: Text `RED`BLDObjective:`BLD Show that a monopoly's marginal revenue is less than the price as a consequence of the price effect.`BLK Whenever a firm sells one more unit of output, total revenue is affected in two ways, the output effect and the price effect. `BLDOutput effect:`BLD Additional revenue resulting from the sale of the additional unit itself. `BLDPrice effect:`BLD Loss in revenue from the sale of all the other units sold resulting from the fact that the monopoly must lower the price in order to sell one more unit. Let us describe the output and price effects more concretely. By default, the monopoly sells 6,000 units of output. `BLDOutput effect:`BLD Additional revenue resulting from the sale of the 6,001th unit itself. `BLDPrice effect:`BLD Loss in revenue resulting from the sale of the 6,000 other units sold because the monopoly must reduce the price in order to sell 6,001 units. `BLDQuestion:`BLD Initially, the monopoly sells 6,000 units at a price of $280.00. Why must the monopoly reduce the price to $279.98 to sell 6,001 units? Hint: What is the slope of the demand curve? `BLDQuestion:`BLD What is the output effect? That is, how much additional revenue will the monopoly collect from the sale of the 6,001th units itself? `BLDQuestion:`BLD What is the price effect? That is, how much will the revenues collected from the other 6,000 units fall as a consequence of the lower price the monopoly must charge? Explain the gap between the monopoly's price and marginal revenue. ` Prob End ` Problem 3 Start Screen 4 - Marginal Revenue, Output Effect, Price Effect, and the Number of Firms // 0: Title // Slider visibility N L B B // 1: Demand intercept, Demand slope, // Firm Quantity, Number of firms // Effects visibility T // 2: Quantity and price visibility // Initial firm quantity 6000.0 // 3: Initial total quantity ` Text Start // 4: Text `RED`BLDObjective:`BLD Show that as the number of firms increase the price effect diminishes and consequently the gap between the price and a firm's marginal revenue also diminishes.`BLK As before, we begin with one firm, a monopoly selling 6,000 units. Check to be certain that your calculations of the price and the monopoly's marginal revenue from the previous screen were correct. Compare the price effect with the gap between the price and the monopoly's marginal revenue. Explain why they are related in this way. Now, let us see what happens when we increase the number of firms in the market. To do so, we will use the new scrollbar that has just appeared in the upper right corner of the screen, the Number of Firms scrollbar. Using the Number of Firms scrollbar, increase the number of firms from 1 to 2. Note that total output remains at 6,000 units; consequently, the price is still $280.00. Output for each of the two firms is half of the total, 3,000. The tables and graph now describes one of the firms. Does the firm's quantity effect change? Does the firm's price effect change? Compare the price effect with the gap between the price and the firm's marginal revenue. Using the number of firms scrollbar, increase the number of firms from 2 to 5. Note that total output remains at 6,000 units; consequently, the price is still $280.00. Output for each of the five firms is a fifth of the total, 1,200. The tables and graph now describes one of the firms. Does the firm's quantity effect change? Does the firm's price effect change? Compare the price effect with the gap between the price and the firm's marginal revenue. Continue to increase the number of firms. Does the firm's quantity effect change? Does the firm's price effect change? Compare the price effect with the gap between the price and the firm's marginal revenue. `BLDQuestion:`BLD As the number of firms increases, what happens to the gap between the price and the firm's marginal revenue? ` Prob End """ }