Question 1 (Essay Worth 10 points) (02.01-02.08 HC) For all...

Question 1 (Essay Worth 10 points) (02.01-02.08 HC) For all graphs, be sure to correctly and completely label all axes and curves and use arrows to indicate the direction of any shifts. Assume that the market for tea is in equilibrium. a. Graph the market for tea, assuming unit-elastic supply and demand. Label the equilibrium price Pe and the equilibrium quantity Qe. b. The price of coffee increases from $5 to $6, and the quantity demanded of tea increases from 40 thousand units to 50,000 units. What is the cross-price elasticity of tea and coffee? c. Are coffee and tea substitutes or complements? Explain using the elasticity coefficient. d. Illustrate the effect of the change in the market for coffee from part (b) on your market graph for tea from part (a), labeling the new equilibrium price and quantity Pe2 and Qe2, respectively. e. What happened to the producer surplus in the market for tea as a result of part (d)? f. On a new graph, illustrate the effect of an effective price ceiling on coffee. Label the price ceiling Pc, and the quantity exchanged with the ceiling Qc. g. Shade the deadweight loss from the price ceiling. h. The pre-ceiling equilibrium price was $4, the price ceiling is $3, and the quantity consumed went from 200 thousand units to 150 thousand units. What is the total amount of revenue lost because of the price ceiling?

Transcript

00:01 Hello, to find the individual short run supply curve equation for the coffee shop, we need to equate marginal cost with the market price.

00:09 So mc is equal to 10q where p is equal to 1000 less 10q.

00:20 Q represents the total market output.

00:23 Setting mc equal to p, here 10q is equal to 1000 minus 10q.

00:38 Simplifying the equation, we will get the value of the small q that will be 50.

00:45 The individual short run supply curve equation for the coffee shop is q small q equals to 50.

00:52 In part b, in long run equilibrium, firms are operating at their efficient scale which occurs when they produce at a minimum average total cost.

01:02 To determine the market price, firm output, number of firms and the market output, we need to equate marginal cost with the market price and set it equal to the minimum average total cost.

01:17 So here mc is equal to p, mc is equal to 10q where p is equal to 1000 less 10q.

01:32 Minimum average total cost occurs when mc equals average total cost.

01:48 So 10 small q is equal to 5 small q.

01:52 Here the value of the q will be 0 .5.

01:57 Substituting q back into the market demand equation to find the market output, market output is equal to 1000 less 10p.

02:10 Q is equal to 1000 less 10 into 0 .5.

02:19 Here the value of q will be 99.

02:24 Since the market output represents the total output of all the firms and we know that each coffee shop produces q is equal to 0 .5, we can calculate the number of firms.

02:35 So number of firms will be equal to q divided by small q.

02:40 N is equal to 995 divided by 0 .5.

02:46 Number of firms will be 1990.

02:50 Therefore, in the long run equilibrium, the market price is equal to 0 .5 dollar.

02:56 The market supply equation is found by the summing up the individual short run supply curves of all the firms.

03:04 Since each coffee shop's short run supply equation is q is equal to 50 and there are n is equal to 1990 firms, the market supply equation will become market supply will be equal to number of firms multiplied by short run supply equation.

03:26 So qs will be equal to 1990 into 50.

03:33 So quantity market supply will be equal to 99500.

03:40 To determine supply elasticity, we need to examine the price elasticity of supply.

03:45 Elasticity is calculated as a percentage change in the quantity demanded divided by percentage change in price.

03:52 So elasticity is equal to change in quantity supplied divided by quantity supplied before into initial price divided by change in the price.

04:11 Since the market supply equation is qs is equal to 99500, it does not depend on price.

04:17 Therefore, the percentage change in quantity supplied will always be zero regardless of any change in the price.

04:22 As a result, the supply elasticity is perfectly elastic.

04:36 To determine consumer surplus, producer surplus and the total surplus, we need to calculate the areas on the supply and the demand graph.

04:44 Consumer surplus is the area between the demand curve and the equilibrium lineup to the equilibrium quantity.

04:50 Producers surplus the area between the supply curve and the equilibrium price lineup to the equilibrium quantity.

04:57 And the total surplus is equal to the sum of consumer surplus and producer surplus.

05:02 Using the demand equation, which is equal to 1000 minus 10p and the supply equation that is q is equal to 50, we can find the equilibrium price and the quantity by setting q equals to small q.

05:25 It will be 1000 less 10p is equal to 50.

05:30 Here we will solve this equation and we will get the value of the p that will be 95.

05:36 Substituting the equilibrium price back into the demand equation to find the equilibrium quantity, we will, it will be 1000 less 10p and quantity will be 1000...

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