The relationship between the short run and the long run

First off, we're going to talk about tangency.

LEFT OF TANGENCY: This is when there is too much capital to efficiently produce a specific quantity of output. In other words, the SRAC > LRAC. This can be corrected by subletting capital (hence moving us into the long run)

Eg: You want to produce 20 letters. You have 3 meters of office space, and two secrataries who each produce 10 letters. Each secratary only requires 1 meter of office space though, so there is an extra meter of office space which is adding an unecessary burden to your overhead costs.

AT TANGENCY: This is when there is exactly the right amount of capital to efficiently produce a given quantity of product. In other words, the SRAC = LRAC. You don't need to change anything, because production is already the most efficient it can be for that level of output.

Eg: You want to produce 20 lettters. You have 2 meters of office space, and two secrataries who each produce 10 letters. Each secratary only requires 1 meter of office space, so this is perfect. There is just the right amount of secrataries and office space to produce 20 letters.

RIGHT OF TANGENCY: This is when there is too little capital to efficiently produce a specific quantity of output. In other words, the SRAC > LRAC. This can be corrected by purchasing capital (hence moving us into the long run)

Eg: You want to produce 30 letters. You have 2 meters of office space, and 3 secrataries who each produce 10 letters. Each secratary requires 1 meter of office space though, so there isn't enough office space for each secratary to do her job most efficiently.

What we can see here is that LRAC is an 'envelope' of all SRAC curves. Each point on the LRAC curve represents a tangency point with a short run cost curve for a different amount of capital. This tangency point is the OPTIMAL level of fixed factor of each output level.

So basically, each different short run cost curve tangent to the long run cost curve represents a different level of capital.

NOTE there is only one point of the entire LRAC curve where the SRAC curve is tangent to the LRAC at it's minimum.

IT IS ALWAYS MORE EFFICIENT FOR FIRMS TO HAVE LOWER COSTS. USUALLY, THIS MEANS BEING TANGENT TO THE LRAC CURVE!

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Deriving the supply curve:

SR:
-One Fixed Factor
-Fixed Prices

LR:
-All Factors Can Vary
-Prices Can Also Vary

Demand can increase independently from supply. As we know, an increase in demand leads to an increase in the price. An increased unit price for products will generate positive economic profits for producers in high-demand industries. This acts as a signal for other firms to enter this industry. As a result, the overall supply for this product will increase.

The long run supply is a conjoined trail of all the points on intersection caused by demand induced shifts in short run supply (thus, the long run supply is not always necessarily upward-sloping).

Long run supply may increase, remain constant, or decease depending factor price changes and the conditions of entry into that particular industry.

The long run average costs for each firm SHIFTS as the industry expands.

Economies of scale determine the shape of the long run average cost curve
Shifts in the long run average cost determine the shape of long run supply