No not necessarily. For example, the price of substitutes such as pork, chicken or lamb may have risen by a larger amount. In such cases the demand curve for beef will have shifted to the right. Thus, although a rise in the price of pork will cause a movement up along this new demand curve, more beef will nevertheless be demanded because beef is now relatively cheaper than the alternatives.
Since in this case the price of the beef has increased simultaneously with the increase in the price of its substitutes, therefore, the demand of beef will increase from Q1 to Q2 even when its price has increased from P1 to P2. Because law of demand holds true when "other things being equal". But in this case "other things being equal" does not true because increase in price of beef is also accompanied by increase in the price of its substitutes.
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