The handmade snuffbox industry is composed of 100 identical...

The handmade snuffbox industry is composed of 100 identical firms, each having short-run total costs given by $$S T C=0.5 q^{2}+10 q+5$$ and short-run marginal costs by $$S M C=q+10$$ where $q$ is the output of snuffboxes per day. a. What is the short-run supply curve for each snuffbox maker? What is the short-run supply curve for the market as a whole? b. Suppose the demand for total snuffbox production is given by $$Q=1,100-50 P$$ What will be the equilibrium in this marketplace? What will each firm's total short-run profits be? c. Graph the market equilibrium and compute total short-run producer surplus in this case. d. Show that the total producer surplus you calculated in part (c) is equal to total industry profits plus industry short-run fixed costs.

The handmade snuffbox industry is composed of 100 identical firms, each having short-run total costs given by $$S T C=0.5 q^{2}+10 q+5$$ and short-run marginal costs by $$S M C=q+10$$ where $q$ is the output of snuffboxes per day.
a. What is the short-run supply curve for each snuffbox maker? What is the short-run supply curve for the market as a whole?
b. Suppose the demand for total snuffbox production is given by $$Q=1,100-50 P$$ What will be the equilibrium in this marketplace? What will each firm's total short-run profits be?
c. Graph the market equilibrium and compute total short-run producer surplus in this
case.
d. Show that the total producer surplus you calculated in part (c) is equal to total industry profits plus industry short-run fixed costs.

Key Concepts

Producer Surplus

Producer surplus is the difference between what producers are willing to accept for a good (as indicated by the marginal cost curve) and what they actually receive at the market price. It is graphically represented by the area above the supply curve and below the equilibrium price, and it provides insight into the benefits accruing to producers from market transactions.

Fixed Costs

Fixed costs are expenditures that do not vary with the level of output in the short run, such as rent, machinery, or other overhead costs. These costs are incurred regardless of the quantity produced, hence playing a key role in short-run cost analysis and affecting a firm's profitability even when production decisions are made based on variable costs.

Profit Calculation

Profit calculation involves determining the difference between a firm's total revenue and its total cost, which includes both variable and fixed costs. In the short run, even if a firm is earning positive revenue, the presence of fixed costs may result in lower profits or even losses. This calculation is critical for firms to assess their performance and make production decisions.

Market Equilibrium

Market equilibrium is the point where the quantity demanded by consumers equals the quantity supplied by producers. In this state, there is no tendency for the market price to change, and it serves as the benchmark for analyzing how external changes affect supply and demand and, consequently, the equilibrium outcome.

Market Supply Curve

The market supply curve is the horizontal summation of the individual short-run supply curves of all firms in the market. It reflects the total quantity of a good that all firms in the industry are willing to produce at different price levels, and it is used in conjunction with the market demand curve to determine the equilibrium price and quantity in the marketplace.

Marginal Cost

Marginal cost represents the additional cost incurred by producing one more unit of output. In microeconomic theory, the marginal cost curve plays a central role in determining an individual firm’s output decision, as profit maximization occurs when marginal cost equals the market price, assuming no price manipulation.

Short-run Supply Curve

In the context of firm behavior, the short-run supply curve is derived from the firm's marginal cost curve above the shutdown point. It shows the relationship between the market price and the quantity of output a firm is willing to supply in the short run, assuming fixed factors of production and that the firm will produce only if the price covers its average variable costs.

Transcript

00:01 So the handmade snuffbox industry is composed of hundred identical firms and each have short run total cost given by the formula we're giving.

00:12 So the first question wants us to find, what is the short run supply curve for each snuff box maker and what is the short run supply curve for the market as a whole? so for this one p is equal to nt is a short run supply cup of an individual frame in a perfect competition so this is a short run supply curve of an individual firm in perfect competition so therefore p is equal to p is equal to q plus 10 and then that's equal to p minus 10 so this is the this is the individual firm supply code so there is there are hundred identical firms in the market right so the market supply would be market supply would be equals to hundred and then this would be android open market p minus 10 and this is equals to 100p minus 1000.

02:39 So this is the market supply code.

02:51 So now moving on to the second question.

02:56 Suppose the demand for total snuffbook production is given by q is equal to 1 ,100 minus 50p.

03:12 What will be the equilibrium in this market and what will each firm's total shots run profits be so for this q is equal to this right so q is equals to 100p minus 1 ,000 which is the market supply that we did and then q is equals to 1 ,100 minus 50p which is what we are giving and this is the market supply that we did and then q is equals to 1 ,100 minus 50p which is what we are giving and this is the market demand so at equilibrium the market supply will be equal to market demand.

04:01 Market supply is equal to market demand.

04:06 So that means to say that 1 ,000 p rather 100p minus 1 ,000 equals to 1 ,100 minus 50p.

04:20 Now if you solve this 150p is equals 2 ,000...

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