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First, we must note that average cost for a given level of output in the long run must be less than or equal to the average cost in the short run. Which means that LRAC must be the outmost curve and no SRAC curve should be allowed to cover any point outside the LRAC. Otherwise we would have a graph like this: (sorry for the terrible drawing)If this were the case, SRAC of producing Q* units of output would be lower in the short run than in long run, which is inconsistent with economic theory. Incosistent because of this: SRAC curves are u-shaped because of initially increasing, eventually decreasing marginal returns, which is not something of concern in the long run. LRAC curve on the other hand, is U-shaped because of initially increasing, eventually decreasing returns to scale. Moreover, in the long run the firm also enjoys economies of scale and suffers diseconomies of scale after the minimum efficient scale ie. the minimum point of LRAC curve. Besides these, in the long run the firm has the advantage of adjusting its scale and tailoring its labour-to-capital ratio to become more resource efficient than the case in the short run.So, if no short-run curve shall be allowed to go beyond the long-run curve, the LRAC curve must cover all the short-run ones as an envelope. That is, the LRAC curve should be tangent to each SRAC curve at a single point. In other words its slope must be equal to the slope of SRAC curves at those points. If LRAC curve were the collection of minimum points of SRAC curves, then its slope should be zero everywhere. But how can a (preferrably differentiable) curve have a U-shape and also zero slope at every point? It simply cannot.The only point at which LRAC intersects an SRAC curve at the minimum point of a SRAC curve is when the firm shoots the bulls eye, or when long-run plans and short-run plans coincide. We call that point minimum efficient scale, that is the minimum point of the LRAC curve.That's simply why.

Long answer ahead.The crucial factors are economies and diseconomies of scale.What are economies of scale?It essentially cost advantages while increasing production. With lower (or constant) inputs, output is increasing by a greater amount.Say with x inputs 2x output is produced leading to higher profits.Now what are diseconomies of scale?Its the opposite, i.e. a cost disadvantage as output is increased. With the given inputs, the output produced is lower leading to lower profits.How is LRAC related to this?We know each firm will produce at minimum cost, so as long as average cost is declining in the long run, the firm will exploit the economies of scale. With scaling up of production, there will be point when the economies of scale have been fully exploited. From this point if production is increased further, the firm will face cost disadvantages and the LRAC curve will start to move upwards.Another Perspective:Cost advantage is reflected in Increasing Returns to Scale—a certain amount of input results in more than double of output. This is the falling portion of LRAC.Cost disadvantage is due to Decreasing Returns to Scale—a certain amount of input results in less than double of output. This will be the rising portion of LRAC.The minimum point of LRAC reflects Constant Returns to Scale where the firm will break even because P=minimum AC is the equilibrium condition in the long run.SRAC & LRAC:LRAC is an envelope of all possible short run average cost (SRAC) curves. LRAC is a locus of the minimum points of all SRAC curves.Be it short or long run, the firm will always prefer to produce at minimum costs. As it scales up output while staying at minimum costs, the long run average cost is nothing but the average of these minimum points of SRAC.Thank you for your time.:)

The answer is pretty simple when you fully appreciate the assumptions of the model. The assumption of perfect information entails that all producers are using the same techniques and inputs. In equilibrium, every producer is then operating at the lowest possible long-run average cost with a normal return (see LRAC). In this case, no producer can offer at a lower price without losing money.Consider a market's "search" for a long-run equilibrium position (with the demand schedule fixed): If all producers are facing the same cost curves then the search involves increasing or decreasing the number of producers until their combined output sets a market supply schedule which sets a price matching the lowest possible LRAC of any competitor (i.e., all competitors). And so it's the number of producers that is the "variable" that provides the solution to the long-run market price and quantity.PS. You should, also, keep in mind that the model applies to commodities only (and so "branding" or other intangible assets are not involved).