in perfect competition the slope of firm's demand curve in horizontal straight line ( AR = AC ) explainplease answer fast

I think you might be asking about the equality between AR and MR. In a perfectly competitive market, the demand curve is shown with a straight horizontal line. This is because in a perfectly competitive market, there are a large number of buyers and sellers and homogenous products. Due to which the sellers do not have any control over the market price. That is, if in case, a firm raises its price then the buyers will shift towards other firms. Thus, the firms do not have control over the prices. Hence, the firm faces infinitely elastic demand curve (i.e. a straight line), which depicts that no matter how many units of output are supplied, the price will remain the same.

Also, in a perfectly competitive market, the AR curve coincides with the MR curve. The reason behind this lies in the fact that in a perfectly competitive market, firm is the price taker and industry is the price maker. That is, the firms has to accept the price set by the industry for the sale of commodities. Thus, in such a case, with the sale of every additional unit of output, the addition to the total revenue (i.e. MR) and the revenue earned per unit of output (i.e. AR) will be equal to the set price. Hence, AR is always equal to MR in a perfectly competitive market and the two curves coincide.

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